How can old debts be paid to people whose whereabouts are unknown, and is forgiving others considered an argument before God for the repayment of these debts?

One must strive to locate the creditors or their heirs to repay the debts. If they cannot be reached, the amount should be given as charity on their behalf. If they are found later, they are given the choice: either to approve the charity, in which case they receive its reward, or to reclaim their rights, and the reward for the charity then goes to the one who gave it.

This is supported by what is stated in Musannaf Ibn Abi Shaybah: from Ibrahim, who said: "If you owe a debt to a man, and you do not know where he is or where his heir is, then give it in charity on his behalf. If he comes, then give him the choice."

It is also reported in Musannaf Ibn Abi Shaybah and in Al-Bukhari (mu'allaqan) that Ibn Mas'ud bought a slave girl, and her owner disappeared. He sought for him for a year, then gave her price in charity, saying: "O Allah, it is for him; but if he refuses, then it is on me and to me." This means: he gets the reward if he approves the charity, and the liability is on me if he does not approve it.

It is mentioned in Mataalib Uli An-Nuha and Majma' Al-Anhar that if someone has debts and grievances and is ignorant of their owners, and despairs of knowing them, then he must give their value in charity from his money, while guaranteeing it to them if they become known.