Creditors can generally collect against an estate, especially on secured loans like mortgages, but they generally can't enforce against relatives. This is a little complicated in that many states still have "filial responsibility" statutes actually on the books, but it's almost unheard of for them to be enforced. The one state that still does, albeit rarely, is Pennsylvania, and the legislature is currently considering doing away with this.
However, because there are such laws, unethical creditors will try to trick people into paying on these debts, so they can then argue they voluntarily assumed them, which is why you never pay these lying fucks a penny without talking to your own lawyer first, who will probably tell you to tell them to go fuck themselves.