Vatican II Documents talking teaching Extra Ecclesiam nulla salus and the necessity of being “bound” and “united” to the Church to be saved.

Ad Gentes

¶7. This missionary activity derives its reason from the will of God, “who wishes all men to be saved and to come to the knowledge of the truth. For there is one God, and one mediator between God and men, Himself a man, Jesus Christ, who gave Himself as a ransom for all” (1 Tim. 2:45), “neither is there salvation in any other” (Acts 4:12). Therefore, all must be converted to Him, made known by the Church’s preaching, and all must be incorporated into Him by baptism and into the Church which is His body. For Christ Himself “by stressing in express language the necessity of faith and baptism (cf. Mark 16:16; John 3:5), at the same time confirmed the necessity of the Church, into which men enter by baptism, as by a door. Therefore those men cannot be saved, who though aware that God, through Jesus Christ founded the Church as something necessary, still do not wish to enter into it, or to persevere in it."(17) Therefore though God in ways known to Himself can lead those inculpably ignorant of the Gospel to find that faith without which it is impossible to please Him (Heb. 11:6), yet a necessity lies upon the Church (1 Cor. 9:16), and at the same time a sacred duty, to preach the Gospel. And hence missionary activity today as always retains its power and necessity.

By means of this activity, the Mystical Body of Christ unceasingly gathers and directs its forces toward its own growth (cf. Eph. 4:11-16). The members of the Church are impelled to carry on such missionary activity by reason of the love with which they love God and by which they desire to share with all men the spiritual goods of both its life and the life to come.

Finally, by means of this missionary activity, God is fully glorified, provided that men fully and consciously accept His work of salvation, which He has accomplished in Christ. In this way and by this means, the plan of God is fulfilled - that plan to which Christ conformed with loving obedience for the glory of the Father who sent Him,(18) that the whole human race might form one people of God and be built up into one temple of the Holy Spirit which, being the expression of brotherly harmony, corresponds with the inmost wishes of all men. And so at last, there will be realized the plan of our Creator who formed man to His own image and likeness, when all who share one human nature, regenerated in Christ through the Holy Spirit and beholding the glory of God, will be able to say with one accord: “Our Father.”(19)

Lumen Gentium

¶¶13..17,48
¶13. All men are called to belong to the new people of God. Wherefore this people, while remaining one and only one, is to be spread throughout the whole world and must exist in all ages, so that the decree of God’s will may be fulfilled. In the beginning God made human nature one and decreed that all His children, scattered as they were, would finally be gathered together as one. (117) It was for this purpose that God sent His Son, whom He appointed heir of all things,(118) that be might be teacher, king and priest of all, the head of the new and universal people of the sons of God. For this too God sent the Spirit of His Son as Lord and Life-giver. He it is who brings together the whole Church and each and every one of those who believe, and who is the well-spring of their unity in the teaching of the apostles and in fellowship, in the breaking of bread and in prayers.(119)

It follows that though there are many nations there is but one people of God, which takes its citizens from every race, making them citizens of a kingdom which is of a heavenly rather than of an earthly nature. All the faithful, scattered though they be throughout the world, are in communion with each other in the Holy Spirit, and so, he who dwells in Rome knows that the people of India are his members”(9*). Since the kingdom of Christ is not of this world(120) the Church or people of God in establishing that kingdom takes nothing away from the temporal welfare of any people. On the contrary it fosters and takes to itself, insofar as they are good, the ability, riches and customs in which the genius of each people expresses itself. Taking them to itself it purifies, strengthens, elevates and ennobles them. The Church in this is mindful that she must bring together the nations for that king to whom they were given as an inheritance,(121) and to whose city they bring gifts and offerings.(122) This characteristic of universality which adorns the people of God is a gift from the Lord Himself. By reason of it, the Catholic Church strives constantly and with due effect to bring all humanity and all its possessions back to its source In Christ, with Him as its head and united in His Spirit. (10*)

In virtue of this catholicity each individual part contributes through its special gifts to the good of the other parts and of the whole Church. Through the common sharing of gifts and through the common effort to attain fullness in unity, the whole and each of the parts receive increase. Not only, then, is the people of God made up of different peoples but in its inner structure also it is composed of various ranks. This diversity among its members arises either by reason of their duties, as is the case with those who exercise the sacred ministry for the good of their brethren, or by reason of their condition and state of life, as is the case with those many who enter the religious state and, tending toward holiness by a narrower path, stimulate their brethren by their example. Moreover, within the Church particular Churches hold a rightful place; these Churches retain their own traditions, without in any way opposing the primacy of the Chair of Peter, which presides over the whole assembly of charity (11*) and protects legitimate differences, while at the same time assuring that such differences do not hinder unity but rather contribute toward it. Between all the parts of the Church there remains a bond of close communion whereby they share spiritual riches, apostolic workers and temporal resources. For the members of the people of God are called to share these goods in common, and of each of the Churches the words of the Apostle hold good: “According to the gift that each has received, administer it to one another as good stewards of the manifold grace of God”.(123)

All men are called to be part of this catholic unity of the people of God which in promoting universal peace presages it. ==And there belong to or are related to it in various ways, the Catholic faithful, all who believe in Christ, and indeed the whole of mankind, for all men are called by the grace of God to salvation==.

¶14. This Sacred Council wishes to turn its attention firstly to the Catholic faithful. Basing itself upon Sacred Scripture and Tradition, it teaches that ==the Church, now sojourning on earth as an exile, is necessary for salvation. Christ, present to us in His Body, which is the Church, is the one Mediator and the unique way of salvation. [comment below] In explicit terms He Himself affirmed the necessity of faith and baptism(124) and thereby affirmed also the necessity of the Church, for through baptism as through a door men enter the Church. Whosoever, therefore, knowing that the Catholic Church was made necessary by Christ, would refuse to enter or to remain in it, could not be saved.==

Docet autem, Sacra Scriptura et Traditione innixa, Ecclesiam hanc peregrinantem necessariam esse ad salutem. Unus enim Christus est Mediator ac via salutis ~LG14§1

[Comment:] “one Mediator and the unique way of salvation” is a bad translation. the Latin says very clearly says “one Mediator and way of salvation”

They are fully incorporated in the society of the Church who, possessing the Spirit of Christ accept her entire system and all the means of salvation given to her, and are united with her as part of her visible bodily structure and through her with Christ, who rules her through the Supreme Pontiff and the bishops. ==The bonds which bind men to the Church in a visible way are profession of faith, the sacraments, and ecclesiastical government and communion. He is not saved, however, who, though part of the body of the Church, does not persevere in charity. He remains indeed in the bosom of the Church, but, as it were, only in a "bodily" manner and not "in his heart."(12*) All the Church's children should remember that their exalted status is to be attributed not to their own merits but to the special grace of Christ. If they fail moreover to respond to that grace in thought, word and deed, not only shall they not be saved but they will be the more severely judged.(13*)==

Catechumens who, moved by the Holy Spirit, seek with explicit intention to be incorporated into the Church are by that very intention joined with her. With love and solicitude Mother Church already embraces them as her own.

¶15. The Church recognizes that in many ways she is linked [“coniunctam”] with those who, being baptized, are honored with the name of Christian, though they do not profess the faith in its entirety or do not preserve unity of communion with the successor of Peter. (14*) For there are many who honor Sacred Scripture, taking it as a norm of belief and a pattern of life, and who show a sincere zeal. They lovingly believe in God the Father Almighty and in Christ, the Son of God and Saviour. (15*) They are consecrated by baptism, in which they are united with Christ. They also recognize and accept other sacraments within their own Churches or ecclesiastical communities. Many of them rejoice in the episcopate, celebrate the Holy Eucharist and cultivate devotion toward the Virgin Mother of God.(16*) They also share with us in prayer and other spiritual benefits. Likewise we can say that in some real way they are joined with us in the Holy Spirit, for to them too He gives His gifts and graces whereby He is operative among them with His sanctifying power. Some indeed He has strengthened to the extent of the shedding of their blood. In all of Christ’s disciples the Spirit arouses the desire to be peacefully united, in the manner determined by Christ, as one flock under one shepherd, and He prompts them to pursue this end. (17*) Mother Church never ceases to pray, hope and work that this may come about. She exhorts her children to purification and renewal so that the sign of Christ may shine more brightly over the face of the earth.

¶16. Finally, those who have not yet received the Gospel are related in various ways to the people of God.(18* [summa]) In the first place we must recall the people to whom the testament and the promises were given and from whom Christ was born according to the flesh.(125) On account of their fathers this people remains most dear to God, for God does not repent of the gifts He makes nor of the calls He issues.(126) But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Muslims, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things,(127) and as Saviour wills that all men be saved.(128) Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience.(19* Feeney, Letter of the Holy Office to the Archbishop of Boston 1949) Nor does Divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with His grace strive to live a good life. ==Whatever good or truth is found amongst them is looked upon by the Church as a preparation for the Gospel.(20* [Eusebius])== She knows that it is given by Him who enlightens all men so that they may finally have life. But often men, deceived by the Evil One, have become vain in their reasonings and have exchanged the truth of God for a lie, serving the creature rather than the Creator.(129) Or some there are who, living and dying in this world without God, are exposed to final despair. Wherefore to promote the glory of God and procure the salvation of all of these, and mindful of the command of the Lord, "Preach the Gospel to every creature",(130) the Church fosters the missions with care and attention.

[S. Thomas, Summa Theol. III, q. 8, a. 3, ad 1] Those who are unbaptized, though not actually in the Church, are in the Church potentially. And this potentiality is rooted in two things—first and principally, in the power of Christ, which is sufficient for the salvation of the whole human race; secondly, in free-will.

¶17. As the Son was sent by the Father,(131) so He too sent the Apostles, saying: “Go, therefore, make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things whatsoever I have commanded you. And behold I am with you all days even to the consummation of the world”.(132) The Church has received this solemn mandate of Christ to proclaim the saving truth from the apostles and must carry it out to the very ends of the earth.(133) Wherefore she makes the words of the Apostle her own: “Woe to me, if I do not preach the Gospel”,(134) and continues unceasingly to send heralds of the Gospel until such time as the infant churches are fully established and can themselves continue the work of evangelizing. For the Church is compelled by the Holy Spirit to do her part that God’s plan may be fully realized, whereby He has constituted Christ as the source of salvation for the whole world. By the proclamation of the Gospel she prepares her hearers to receive and profess the faith. She gives them the dispositions necessary for baptism, snatches them from the slavery of error and of idols and incorporates them in Christ so that through charity they may grow up into full maturity in Christ. Through her work, whatever good is in the minds and hearts of men, whatever good lies latent in the religious practices and cultures of diverse peoples, is not only saved from destruction but is also cleansed, raised up and perfected unto the glory of God, the confusion of the devil and the happiness of man. The obligation of spreading the faith is imposed on every disciple of Christ, according to his state.(21*) Although, however, all the faithful can baptize, the priest alone can complete the building up of the Body in the eucharistic sacrifice. Thus are fulfilled the words of God, spoken through His prophet: “From the rising of the sun until the going down thereof my name is great among the gentiles, and in every place a clean oblation is sacrificed and offered up in my name”.(135)(22*) In this way the Church both prays and labors in order that the entire world may become the People of God, the Body of the Lord and the Temple of the Holy Spirit, and that in Christ, the Head of all, all honor and glory may be rendered to the Creator and Father of the Universe.

¶48. The Church, to which we are all called in Christ Jesus, and in which we acquire sanctity through the grace of God, will attain its full perfection only in the glory of heaven, when there will come the time of the restoration of all things. At that time the human race as well as the entire world, which is intimately related to man and attains to its end through him, will be perfectly reestablished in Christ.(238)

Christ, having been lifted up from the earth has drawn all to Himself.(239) Rising from the dead(240) He sent His life-giving Spirit upon His disciples and through Him has ==established His Body which is the Church as the universal sacrament of salvation.== Sitting at the right hand of the Father, He is continually active in the world that He might lead men to the Church and through it join them to Himself and that He might make them partakers of His glorious life by nourishing them with His own Body and Blood.

Gaudium et spes

¶22
-22. The truth is that only in the mystery of the incarnate Word does the mystery of man take on light. For Adam, the first man, was a figure of Him Who was to come,(20) namely Christ the Lord. Christ, the final Adam, by the revelation of the mystery of the Father and His love, fully reveals man to man himself and makes his supreme calling clear. It is not surprising, then, that in Him all the aforementioned truths find their root and attain their crown.

He Who is “the image of the invisible God” (Col. 1:15),(21) is Himself the perfect man. To the sons of Adam He restores the divine likeness which had been disfigured from the first sin onward. Since human nature as He assumed it was not annulled,(22) by that very fact it has been raised up to a divine dignity in our respect too. For by His incarnation the Son of God has united Himself in some fashion with every man. He worked with human hands, He thought with a human mind, acted by human choice(23) and loved with a human heart. Born of the Virgin Mary, He has truly been made one of us, like us in all things except sin.(24)

As an innocent lamb He merited for us life by the free shedding of His own blood. In Him God reconciled us(25) to Himself and among ourselves; from bondage to the devil and sin He delivered us, so that each one of us can say with the Apostle: The Son of God “loved me and gave Himself up for me” (Gal. 2:20). By suffering for us He not only provided us with an example for our imitation,(26) He blazed a trail, and if we follow it, life and death are made holy and take on a new meaning.

The Christian man, conformed to the likeness of that Son Who is the firstborn of many brothers,(27) received “the first-fruits of the Spirit” (Rom. 8:23) by which he becomes capable of discharging the new law of love.(28) Through this Spirit, who is “the pledge of our inheritance” (Eph. 1:14), the whole man is renewed from within, even to the achievement of “the redemption of the body” (Rom. 8:23): “If the Spirit of him who raised Jesus from the death dwells in you, then he who raised Jesus Christ from the dead will also bring to life your mortal bodies because of his Spirit who dwells in you” (Rom. 8:11).(29) Pressing upon the Christian to be sure, are the need and the duty to battle against evil through manifold tribulations and even to suffer death. But, linked with the paschal mystery and patterned on the dying Christ, he will hasten forward to resurrection in the strength which comes from hope.(30)

All this holds true not only for Christians, but for all men of good will in whose hearts grace works in an unseen way.(31 [this cites LG16]) For, since Christ died for all men,(32) and since the ultimate vocation of man is in fact one, and divine, we ought to believe that the Holy Spirit in a manner known only to God offers to every man the possibility of being associated with this paschal mystery.

Such is the mystery of man, and it is a great one, as seen by believers in the light of Christian revelation. Through Christ and in Christ, the riddles of sorrow and death grow meaningful. Apart from His Gospel, they overwhelm us. Christ has risen, destroying death by His death; He has lavished life upon us(33) so that, as sons in the Son, we can cry out in the Spirit; Abba, Father(34)

TLDR

Extra Ecclesiam Nulla Salus must be read as the Church understands it.
Similar to, and expanding upon, the letter concerning Fr. Feeney.