All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
The inheritors of your uncle must pay the debt of their testator from the capital of his estate, if he left any. If he did not leave any money or property, then it is recommended for them to settle his debt from their own money. If the deceased did not leave money and his inheritors did not pay his debt voluntarily, then the case of guarantor (your father) must be considered. If he guaranteed to bring your uncle to the creditor without paying the money on his behalf, then his guarantee is void by the death of your uncle, according to the majority of scholars. Consequently, your father is not liable for doing anything. However, if your father guaranteed to settle the debt on behalf of your uncle because your uncle could not settle the debt due to not having the financial resources, or he died, or any other reason, then your father is liable to pay this money to the due claimant or his inheritors. If he could not find them despite exhaustive searching, then he must give the money as charity for their sake. If the due claimant or his inheritors are found afterwards, they must be given the option of whether to approve the charity, for which they will be rewarded, or receive their money. In the latter case, your father will be rewarded for the charity.
Allaah Knows best.