Curious whether they own it if OPs name is not on the deed. If OP makes payments on it as part of the estate and rented it out does that constitute the estate owning it or does it become defacto ownership if the deed was given to heir as part of the estate and there was no disclaimer of ownership filed? If you send a death cert to the resort and they see that it has been years and you are listed as an heir could they make a claim?
Would love a lawyer like
@LeslieDet to weigh in on this [in general of course] OP needs a lawyer.
If the resort does not have OPs social security number then perhaps they can let it go to foreclosure without credit repercussions because OP could claim to credit agencies that it was never in his/her name. The resort would incur heavy legal fees to prove otherwise so might let it go since the estate kept the payments current. I would definitely speak with a lawyer to try to negotiate deed in lieu with the resort.
I am assuming this is in Florida given hurricane damage. If it is still in the name of the person who died and resort refuses deed in lieu then let it go. Do not object to foreclosure or they may go after back-payments see the timeshare sticky on state laws. But I would consult a lawyer for your specific situation because it is complicated. Give them the Florida (or whatever state it is located) TS laws from the sticky so you are not paying for them to research this.