Under US law, the debts die with the person. You are under no obligation to repay your parent's debts. Now if the debt is tied to a house (mortgage) or a car (car loan), you might lose the house/car if you don't pay, but you do not have an obligation to pay. Likewise failure to pay will not impact your credit.

So if I die in debt up to my eyeballs, and if I am sole signatory on those debts, I have only hurt my creditors, not my family.

caveats-- if my family was counting on the house and I have an unaffordable mortgage, then yes I have caused them harm. Likewise other irresponsible debts.

-- at the end of the chain, creditors are also people. It is their job to loan money at risk, so their loss is their problem, but this assumes I was dealing in good faith when I took the loan.