First of all, it’s not going to happen. But if it did, assuming there were at least one priest left in the world, according to Ott’s Fundamentals of Catholic Dogma, he could ordain other men as priests, and then they could ordain, and so on. (Yes, I was surprised by this too.) The only assumption to be made — and this is a big assumption — is that the permission of the Pope, needed for validity, would be supplanted by epikeia, put another way, Almighty God would not demand the impossible, and this permission would “supply itself”. Ott did not go this far, and I’m not totally comfortable doing it myself. But here is the relevant passage:
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A few years back, a traditionalist priest (Father Lucian Pulvermacher), with valid faculties that had never been revoked (long story), got a “conclave” of laymen to elect him Pope (another long story). As “Pius XIII”, a priest but no bishop, he ordained another man as priest, then as bishop (not sure how this worked), then gave this “bishop” permission to consecrate him as bishop, and, in his mind, reinstated a traditional episcopate (and the papacy while he was at it). It was as though he “restored the true Church” by means of sacramental jumper cables! You can’t make this stuff up. Actually, I read his web pages (to keep up with the goings-on, not to embrace his “true Catholic Church”), and he was a very endearing man, wrote some good things, seemed like a kind, sincere sort. There was a winsomeness to it all. I hated to hear of his passing. His rump “true Catholic Church” did not survive.