Is a Son Responsible for His Father's Debt in Islam?
Question

My father borrowed some gold jewellery from his wife to build a house for me, without my knowledge. Please note that I sent him the costs of construction, and I asked him whether there was anything left of the money, and he told me no. Then after my father died, his wife told me that my father had borrowed the jewellery from her, and he said to her in the presence of my sisters: Take back what is owed from my son. My sisters testify to that. She said that there were papers documenting that, but she lost them; they listed the different weights of the jewellery. What am I obliged to do? If the answer is that I have to pay it, then should I pay the current price of the gold, or the price as it was six years ago? Please note that I do not live in the house, because it was destroyed as a result of war.
Praise be to Allah.Islamic Ruling on Inheriting Debt
If you are sure that your father’s wife’s claim is true, especially since there is testimony from your sisters about your father’s instructions, then you must pay off this debt to her, but it should be paid from the estate, before it is divided.
In other words, the debt should be paid off from what your father left behind of money or property, because it is a debt that is owed by him, and it is not owed by you, because – according to what is mentioned in the question, you did not appoint him to borrow it on your behalf and you did not ask him to do that; rather you were unaware of this debt until after he died.
As that is the case, you are not required to do anything. If your father told others that he had borrowed it for your sake, he had no right to do that according to Islamic teachings.
Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
The heirs are not obliged to pay off the debt [of the deceased]; rather it must be paid from his estate.” (End quote from Minhaj As-Sunnah,  5/232)
When Is a Son Obligated to Pay His Father’s Debt?
If your father did not leave behind any wealth after he died, the heirs are not obliged to pay off this debt.
But our advice to you is to pay off this debt on your father’s behalf from your own wealth, especially if he did not have sufficient wealth to pay it off and you can afford to pay it. That will be a way of showing kindness to him after his death, because his aim was to help you and make things easier for you. Hence the least you could do is respond to kindness with kindness and pay off what he asked you to pay off, according to the testimony of your sisters.
It was narrated that Abu Usayd (may Allah be pleased with him) – said: Whilst I was sitting with the Messenger of Allah (blessings and peace of Allah be upon him), an Ansari man came to him and said: O Messenger of Allah, is there anything left that I could do to honour my parents after their death?
He said: “[There are] four things: offering supplication for them, praying for forgiveness for them, fulfilling their promises, honouring their friends, and upholding ties of kinship, for you have no ties of kinship except through them. These are the things that remain, through which you may honour them after their death.” (Narrated by Imam Ahmad in Al-Musnad, 25/457)
Fulfilling their promises includes carrying out the instructions that your father gave. Even though this is not obligatory for you, as noted above, it comes under the heading of showing kindness to your father and honouring him. And you will have reward with Allah, may He be Glorified.
Pay off the debt according to the price of gold on the day when you want to pay it off, not the date on which the loan was given. Or you can give the same amount of gold, which is better.
For more details, please see the following answers: 200127, 298628, 39175, 201975.
And Allah knows best.