Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, and he answered as follows:
Praise be to Allaah, Lord of the worlds, and peace and blessings be upon our Prophet Muhammad and upon his family and companions, and upon those who follow them in truth until the Day of Judgement. The obligatory Hajj comes first, because he is not obliged to pay off his father’s debts, but if the father left anything behind, this should be used to pay off the debts. If he did not leave anything, then the matter is up to Allaah. The son should rest assured that if the father took money from people with the intention of paying it back, then Allaah will see to it that it is paid back to the one who lent it, so he should not feel anxious or guilty. In conclusion, therefore, he should do his Hajj because he is able to. And Allaah knows best.