Next of kin don’t take up debts unless they’re co-signatories. The assets of the deceased generally go to the creditors first, yes, nullifying any inheritance the next of kin may have been in line for, but the inheritance doesn’t then run in reverse if those assets aren’t enough to cover the debt.

That won’t stop the creditor from trying any trick in the book to get the next of kin to pay, including lying about it, but I’d like to hear of a jurisdiction where the next of kin are legally liable.