Do the heirs have to repay the debt of their deceased uncle – which was an interest-based loan – after the death of his guarantor, their father, knowing that the remaining amount is the usurious interest, and that their uncle does not own any property to repay his debt?

A loan is a transaction legislated for beneficence, and it is not permissible for the lender to take interest on it, because it is usury (riba). It is not permissible for the borrower to pay this interest unless compelled to do so. And if you do not do so (forsake riba), then "be informed of a war from Allah and His Messenger. But if you repent, you may have your principal – [thus] you do no wrong, nor are you wronged." This means do not take an increase, and your wealth should not be diminished. Repaying this interest is not legally binding, and it is not permissible to repay it voluntarily.