There is specific Catholic teaching based on this contingency. There are near prophetic Catholic writers discussing this, early in 20th century. Stunning when I read it. I can get if u want . Father Berry on novusordowatch site.

Sedevacantism bishops are quite clear they have no ordinary jurisdiction. CMRI and SGG seem to have a disagreement on annulments, not sure. There is confusion, and some clergy and laity , some, are making mistakes. If this makes some non Catholic, so be it. Others remain Catholic. Japanese forced out Catholic priests... After a couple hundred yrs, when they returned, the laity had remained Catholic! They were certainly "sloppy" in some areas, to be sure. I'm extremely "sloppy". I have missed formation, I see priest once a mo. But I'm Catholic.

The Church "supplies jurisdiction" using epikeya. Canon law is for salvation of souls. In special circumstances, it can be thrown out. These are extremely dire circumstances