How can a debtor pay off old debts to people, some of whom have died or whose whereabouts are unknown?

The debts you owe to people do not lapse with the passage of time. You must pay them to their owners if they are alive, or to their heirs if they have died. By paying the heirs, your obligation is cleared. However, if they have no heirs or you despair of finding them, then give these debts as charity on behalf of their owners.