Is it permissible to withhold assistance from a relative who took out an interest-based loan and mismanaged his money, leading to an accumulation of debts?

Borrowing with usury is among the destructive sins that bring a curse upon the one who commits it, and it may be the cause of your relative's straitened circumstances. He must hasten to sincere repentance. As for cutting off aid to your relative, you should not do that, because it is a matter of maintaining kinship ties. His poor management should not prevent you from maintaining ties with him through financial assistance, citing the words of Allah Almighty: "And let not those among you who are blessed with graces and abundance swear not to give (any longer) to their kinsfolk, the needy, and those who migrated in the cause of Allah. Let them pardon and overlook. Would you not like that Allah should forgive you? And Allah is Oft-Forgiving, Most Merciful" (An-Nur: 22).