Are you considered responsible for settling your deceased partner's debt if his brothers fail to pay it, or does the debt remain the responsibility of his family, especially after you pledged to pay it and then it became clear that he has sufficient funds for that?

If someone takes on a debt for a deceased person, they are obliged to fulfill that commitment, whether the deceased left behind wealth or not. They can, however, seek reimbursement from the person for whom they stood surety if it becomes clear that the latter did possess wealth. The proof for this is the saying of the Messenger of Allah, peace and blessings be upon him, "Now his skin has become cool," when he learned that the debt had been paid off. If the deceased was insolvent and the guarantor knew of their insolvency, then their assumption of the debt is a voluntary donation, and they cannot seek reimbursement from the deceased even if wealth is found for the latter later on. However, if they knew the deceased had wealth, or thought so, or doubted, and then wealth appeared for them, they have the right to seek reimbursement for what they paid. The heirs of the deceased must pay off the debt before distributing the inheritance. If they do not do so, the guarantor must pay the debt and then seek reimbursement from the heirs.