Children Paying the Debts of Their Dead Parents

Remarkably, one is accounted by Allah according to one’s intention. In other words, if someone borrowed money from others with the intention of paying them back, then Allah will pay them for him/her; whereas if someone took a loan from people with a bad intention, then Allah would persecute him/her. In like manner, if a person dies with the intention of paying the debts but failed to do so, then he/she is not to be accounted. Nevertheless, the heirs should relieve the dead by paying his/her debts because the debt imprisons the dead and hinders him/her from entering Paradise.
Furthermore, the children of the deceased should pay his/her debts, each according to his/her ability. While it is not a must for children to pay back their dead parents’ debts, yet if they don’t do so they would leave their parents to face a torment which only Allah knows about. Such a deed is far away from kindness to one’s parents.
If the deceased left an inheritance, then his/her debts should be paid from it before it is distributed among the heirs.
Dr. Muhammad Sulayman Al-Manee`i, Professor of Islamic studies at Umm Al-Qura University, states the following: You should pay your father’s debts before distributing the property. You can also sell the land left by your father at a lower price so as to sell it speedily.

Having stated the above, I should stress here that you are not asked to pay the debt from your own income. However, if you are well-off, you can pay the debt from your own money then retrieve it from the inheritance afterwards.
Jabir narrated a hadith about a man who passed away while owing a debt of two dinars. Thus, Allah’s Messenger (peace and blessings be upon him) did not perform the funeral prayer on him. Abu Qatadah (may Allah be pleased with him) said that he would pay the debt. When Abu Qatadah paid the debt of the deceased, Allah’s Messenger (peace and blessings be upon him) said that the man was then relieved.
To cut it short, if you are not able to pay the debt from your own income, then you can ask the people whom your father was indebted to, to forgive your father so that he may be relieved from the punishment in the Hereafter.