Generally, debts of a person who has died are the responsibility of the estate of that person. Assets of the estate, such as real estate, property, bank accounts, securities, valuables, and so on will be ordered by the probate court to be sold to pay debts before anything in the estate would go to heirs.
If assets of the estate are not sufficient to pay those debts, the estate is declared to be insolvent (bankrupt), and the creditors will normally write these debts off. If there are some heirs in the picture, some creditors might exert pressure on the heirs to pay the debts, but there is no legal requirement for the heirs to do so.
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