Most types of debt do not die with the debtor. If there are any assets in the estate, then the estate is responsible to pay those debts.
The executor of the estate is required to notify any known creditors that the debtor has passed away and then to pay the debt, if possible.
However, no creditor should ever rely on an executor doing so. The debt might not be known or the executor might not know what his responsibilities are.
Creditors who learn that a debtor has passed away, should take affirmative steps to file a claim against the estate, which must be done following proper procedures. Things can get even more complicated, if the deceased put all of his or her assets in a trust, leaving nothing in an estate.
Under such circumstances the creditor needs to file against the trust, as the NWI Times points out in "Filing claims against a trust."
Filing a claim against a trust, can be even more complicated than filing against an estate, or maybe not.
It depends on the state. Every state has its own laws and procedures that need to be followed for a creditor to properly file a claim to receive the debt of a debtor who has passed away.
For this reason, it is extremely important for creditors to contact a local estate attorney to help them with the process. This is something that must be done without delay, since the statutes of limitations for these claims are often very short, again depending on the state
Reference: NWI Times (July 2, 2017) "Filing claims against a trust."