[havblue]

I guess if you inherit a timeshare you can just insist that it goes to a sibling. Or, even better, a step-sibling...

[loaph]

You can also tell probate court that you refuse the inheritance. You can't be forced to inherit something

[Volundr]

You can, but there is specific paperwork you have to file and you have something like 90 days to do it. And then the next person in line has to, and the next.

Unless everyone is on the ball and actively refuses it, someone gets stuck with it.