Obviously it's a messy affair.
Personally I'd assume that most covenants would not be especially concerned if a twilight happens and wait a full year to see what happens. Most twilights resolve in that span of time.
If the one year elapses and the magus doesn't return, then you consider contacting the magus' filii. Because it's going to be at least 6 more years for the twilight to resolve, and somebody has to manage his affairs in absentia. He may have vis sources that need harvesting, minions/creatures that need managing, and his laboratory might fall into disrepair on its own. The covenant is 'probably' within their rights to keep this sort of thing in-house for the first seven year period, though honestly the redcaps are going to find out because they generally hand deliver messages to the magus in question.
Probably the best course is to inform the filii that the magus has gone into prolonged twilight and that the covenant will monitor the situation. I assume this would be done by general announcement at tribunal and maybe a quaesitor is assigned to monitor the situation.
Once seven years have passed, however, the filii can probably start pressing legal claims. Certainly magi do come back from twilights longer than seven years, but there's a good chance it's final twilight and a covenant can't stonewall forever. On the covenant's side, they might wish to be absolved of the problem (free up lab space, get rid of the monsters in the basement, etc), but this depends on the relationship between the covenant and the filii in question. Older magi might also leave instructions for such a circumstance with the covenant, redcaps or quaesitors.
Once two tribunal cycles have come and gone (meaning the magus in question could be in twilight for over 20 years if they went into twilight shortly after a tribunal), its highly likely they are never coming back and the covenant had better start surrendering stuff to the filii.
If the magus DOES come back from twilight later, well, he's going to have to get his stuff back from the filii. This is probably going to get really messy really quick, as the filii in question probably are in their prime while the magus is likely in decline from late-stage twilight episodes. If everyone is sane and reasonable the magus probably gets his important objects back but has to default on stuff like vis, especially if the tribunal rubber stamped the inheritance moving forward.
If people aren't sane and reasonable, it's wizard's war. People generally don't want to give stuff back after owning it for a decade or more. If the magi involved are Tytalus, well, things get epic.