Is there a solution for debts owed by the deceased that are unknown to the heirs and their creditors?

You are not legally obligated to demand anything except the repayment of known debts owed by your father, and the original presumption is the absolution of his financial liability. You can inquire about his debts among his friends and acquaintances, just as the Companions did. If someone claims a debt and provides evidence, pay it from his estate; otherwise, nothing is incumbent upon you.