"Sedevacantism" is the belief that the See of Rome is currently vacant; that is, there is no current Pope. There are not very many people who believe it, but they do seem to be pretty vocal on the Internet. One thing that I don't understand about it is: What do they think will or should happen in the future in order to resolve the situation? (Of course, the non-sedevacantist majority don't think there's a situation to be resolved at all.) The bulk of what I've read consists of their detailed complaints about recent Popes, along with some wrangling about election procedures and the like; but I haven't seen much that's about the future.
I understand that some of these groups have tried to elect their own Popes. Do they think that the global Church will/should come around to their position? Is there any kind of plan for how this might happen? Or are they content to remain as an elite minority while everybody else is condemned?
I ask partly because I have a sense that there is an eschatological dimension. The contemporary movement reminds me of the late mediaeval apocalyptic theory of an usurping pseudo-papal antichrist and his battle with the true Pope, this being one of the signs of the end of history. (See for example Bernard McGinn, Apocalypticism and Church Reform 1100-1500, in vol. 2 of The Encyclopedia of Apocalypticism, 2000.) I have seen sedevacantists talking about the so-called Prophecy of the Popes, which has quite an end-of-the-world flavour.