A temporarily closed canon can be drawn from a few passages. Here is a logic chain for when the canon would be completed and when it would be reopened in the Christian Greek Scriptures.
"Love never fails. But if there are gifts of prophecy, they will be done away with; if there are tongues, (That is, miraculous speaking in other languages.) they will cease; if there is knowledge, it will be done away with. For we have partial knowledge and we prophesy partially, but when what is complete comes, what is partial will be done away with. When I was a child, I used to speak as a child, to think as a child, to reason as a child; but now that I have become a man, I have done away with the traits of a child. for now we see in hazy outline (or "indistinctly.") by means of a metal mirror, but then it will be face-to-face. At present I know partially, but then I will know accurately, (or "fully.") just as I am accurately known. Now, however, these three remain: faith, hope, love; but the greatest of these is love." 1 Cor 8-13
Paul likened the Christian arrangement of things to a child that would grow up. Once it grew up special gifts of the spirit would cease, but faith, hope and love would remain. What were these special gifts? Some are listed here. But they are broken down more thoroughly in the chapter prior.
"Now there are different gifts, but there is the same spirit; and there are different ministries, and yet there is the same Lord; and there are different activities, (or "operations.") and yet it is the same God who performs them all in everyone. But the manifestation of the spirit is given to each one for a beneficial purpose. For to one is given speech (or "a message.") of wisdom through the spirit, to another speech of knowledge according to the same spirit, to another faith by the same spirit to another gifts of healing by that one spirit, to yet another operations of powerful works, to another prophesying, to another discernment of inspired expressions, to another different tongues, (or "languages.") and to another interpretation of tongues. But all these operations are performed by the very same spirit, distributing to each one respectively just as it wills." - 1 Cor 12:4-11
Note that one of these early gifts was "discernment of inspired expressions." After Christianity leaves its infancy, there would no longer be anyone that could discern directly what was inspired writings and what was correspondence that was limited in use to the audience it was written to. The last of the 12 apostles died near the end of the 1st century. John was used to contribute a gospel, a book of prophetic visions, and 3 letters to the canon somewhere around 96-98 C.E. Once he died there would be no one we could reliably look to as one that had this early gift of "discernment of inspired expressions". "What is complete" would have arrived.
Now post-Armageddon it would be a different story. Re 20:12 points to a time when scrolls not yet opened will be revealed. As yet imperfect mankind will be judged according to how they respond to the things written in them.
"And I saw the dead, the great and the small, standing before the throne, and scrolls were opened. But another scroll was opened; it is the scroll of life. The dead were judged out of those things written in the scrolls according to their deeds." - Re 20:12