Riyad-us-Saliheen 943
Abu Hurairah (May Allah be pleased with him) reported: The Prophet (PBUH) said, "The soul of the deceased believer remains pending on account of the debt till it (the debt) is repayed."
[At-Tirmidhi]
The Divine decision regarding the redemption or punishment of a dead man remains suspended till the time his debt, if any, is paid off. A bereaved family is supposed to give top priority to the clearance of a debt.