Nicene and Post-Nicene Fathers, Vol. IV:
Writings in Connection with the Donatist Controversy.: Chapter 18

Chapter 18.—24.  Whence Cyprian himself 1517 again admonishes us with the greatest fullness, that many who were dead in their trespasses and sins, although they did not belong to the body of Christ, and the members of that innocent and guileless dove (so that if she alone baptized, they certainly could not baptize), yet to all appearance seemed both to be baptized and to baptize within the Church.  And among them, however dead they are, their baptism nevertheless lives, which is not dead, and death shall have no more dominion over it.  Since, therefore, there be dead men within the Church, nor are they concealed, for else Cyprian would not have spoken of them so much, who either do not belong at all to that living dove, or at least do not as yet belong to her; and since there be dead men without, who yet more clearly do not belong to her at all, or not as yet; and since it is true that "another man cannot be quickened by one who himself liveth not,"—it is therefore clear that those who within are baptized by such persons, if they approach the sacrament with true conversion of heart, are quickened by Him whose baptism it is.  But if they renounce the world in word and not in deed, as Cyprian declares to be the case with some who are within, it is then manifest that they are not themselves quickened unless they be converted, and yet that they have true baptism even though they be not converted.  Whence also it is likewise clear that those who are dead without, although they neither "live themselves, nor quicken others," yet have the living baptism, which would profit them unto life so soon as they should be converted unto peace.

Footnotes

In this and the following chapter, Augustin is examining the seventy-first epistle of Cyprian to his brother Quintas, bishop in Mauritania.  Here LXXI. 1.