I am a lawyer and I can briefly explain a few things, with the obvious caveat that this should not be construed as legal advice, all individual situations can vary, and if you believe you may need legal advice, you should contact an attorney.
1. There is generally no way to force someone to accept an inheritance. If someone leaves you a timeshare, whether through their estate plan or via the intestacy laws if your state, you don’t have to take it. But, if you do accept the title or deed, then yeah, it’s yours and you’re on the hook for MF’s, etc.
2. With regard to any debt of a decedent (credit card, TS, car loan, etc.), it is common and accepted practice to see if someone else will assume the debt. A perfect example, my father-in-law died 10 years ago, and he owed balances on 3 credit cards. As soon as the companies discovered he was dead, they call and ask questions like, “will you be making arrangement to assume the balance?” Or, “is anyone accepting the payments?” This is legal. They are hoping a grieving spouse or child will assume they have a legal duty to pay their loved one’s debts. They don’t. But as soon as that person says “yes.” On a recorded line, there is a significant argument that they’ve assumed that debt. For this reason, I took all of these calls, rather than my MIL. And the answer is no. The estate is responsible for the debt, but most creditors know the average American estate is $0. So, yes, they can file a claim in probate against the estate, however, most won’t. They have built into their business model this portion of uncollectible debt.
3. Paying on a debt that is past the statute of limitations can reset that statute of limitations. Debt collectors, again, prey on folks ignorance of the law. The average person doesn’t know the statute of limitations for collecting on a debt in their state, nor do they know the requirements of the Fair Debt Collections Practices Act.