There is no such doctrine. That it doesn't exist doesn't change any facts. It's like asking if doctrine existed specifically to deal with the Western schism and antipopes - that's probably also the best case to look at to guess how things might resolve themselves. If one denies valid orders to the Novus Ordo bishops, it becomes more difficult to imagine.
I'll tell you what wasn't anyone's position during those times, though: we recognise you as the true pope but refuse to submit to you and your teaching.
Are you sure that there's no doctrine on how to deal with those who are in schism? I'm pretty sure that there is.
The situation with the anti-popes is a different situation.
There HAS to be a method (Church teaching), if you are going to adopt the Ipso Facto methodology on how to deal with a heretic Pope, after he is proclaimed by laypersons to no longer be the Pope. Though, of course, there is no doctrine which says that laymen are to proclaim and judge that the Pope is not a Pope, much less on how to treat the non-Pope after laypersons proclaim he is not the pope. Sedes try to force others to adopt their view, through intimidation. What Church teaching says that this behavior is acceptable and needed?
You are venturing into unknown territory when dealing with a heretical Pope, and yet you sedes act as if the there's a specific doctrine that says that laypersons are to judge and proclaim as to whether the seat is empty or not.