Heirs’ Responsibilities After a DeathNone of us like to think about our own or our loved ones’ mortality, but ignoring that eventuality will not make a stressful situation any easier. The creditors cannot then go after the heirs — unless they were cosigners on any of the debts. When there is no money in the estate to pay off a credit card debt, creditors will generally close the account and forgive the debt. However, as with any other debt, the estate must pay any taxes owed before heirs can claim their inheritance. The Bottom LineKnow your rights and responsibilities before you have to deal with the fallout of a death in the family.