Is it religiously obligatory for the sons of the guarantor to pay the loan amount to the bank to clear their deceased father's liability, instead of the sons of the original debtor?

The death of the guarantor does not invalidate the guarantee. The heirs are obligated to pay the guaranteed debt from the inheritance if the claimant demands it. It is stated in Al-Insaf by Al-Mardawi: "And the madhhab (definition) (ruling) applies whether alive or dead." If the deceased did not leave behind enough to cover the debt, then their heirs are not obligated to pay it.