Is there salvation outside the church?

Origen of Alexandria c. 185–c. 254 ADHomilies on Joshua 3.5

Let no one, then, persuade himself, let no one deceive himself: outside this house, that is, outside the Church, no one is saved. If anyone goes outside, he becomes guilty of his own death.

On Rahab's house in Jericho (Joshua 2): everyone in the house, marked with the scarlet cord, is saved when the city falls. Origen reads the house as the Church and the cord as the sign of Christ's blood, in the sentences just before this one. The homilies survive in Rufinus's Latin; the text is Baehrens's edition (GCS 30, 1921), read from the raw scan text in the library's Joshua book, whose locked sections still hold working summaries, so this passage still wants a locked library section.

Cyprian of Carthage c. 200–258 ADOn the Unity of the Church 6

He cannot have God for his Father who does not have the Church for his mother. If anyone could escape who was outside Noah's ark, then he too escapes who is outside the Church.

Written against schism at Carthage and Rome.

Augustine of Hippo 354–430 ADOn Baptism, against the Donatists 4.17.24

There is no salvation outside the Church. Who denies it? And so whatever belongs to the Church has no value for salvation outside the Church. But it is one thing not to have, another not to have to profit.

Augustine accepts the rule, and adds that the Church's sacraments can exist outside it without saving.

Council of FlorenceCantate Domino (Decree for the Jacobites) Denzinger 714

It firmly believes, professes and preaches that no one outside the Catholic Church, not only pagans but also Jews and heretics and schismatics, can share in eternal life, but will go into the eternal fire prepared for the devil and his angels, unless before the end of life they are joined to her. ... No one, however great his almsgiving, even if he sheds his blood for Christ's name, can be saved unless he stays in the bosom and unity of the Catholic Church.

The bull Cantate Domino (4 February 1442), the decree for the Jacobites (the Coptic Christians of Egypt) at the Council of Florence, as printed in Denzinger's Enchiridion (11th edition, 1911), no. 714. It restates, in its strictest conciliar form, the rule Origen pictured and Cyprian coined, drawing on Fulgentius of Ruspe.

Westminster AssemblyWestminster Confession of Faith 25.2

The visible church, which is also catholic or universal under the gospel (not confined to one nation, as before under the law), consists of all those throughout the world that profess the true religion; and of their children: and is the kingdom of the Lord Jesus Christ, the house and family of God, out of which there is no ordinary possibility of salvation.

Protestants too kept the rule, applied to the visible church of all who profess the true faith.

Pius IXAllocution Singulari quadam 9 December 1854

It must be held by faith that outside the Apostolic Roman Church no one can be saved ... But it must likewise be held as certain that those who labor in ignorance of the true religion, if that ignorance is invincible, are not bound by any guilt in this matter before the eyes of the Lord.

The modern Catholic reading keeps the rule and excepts those not at fault.

Second Vatican CouncilLumen Gentium 16

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.

Section 14 of the same document says those who know the Church is necessary and refuse to enter it cannot be saved.