Is it permissible for one of the deceased's relatives to pay off his entire debt to prevent his soul from being suspended, instead of his children paying it off in installments?

Repaying the debt of the deceased is obligatory for their heirs from their estate, because it is a right for the creditors therein, and the deceased is not absolved until it is paid. The debt must be repaid before distributing the inheritance and before executing any will.

If the deceased did not leave enough to repay their debt, and one of their relatives or others volunteers to pay it, that is sufficient and valid on their behalf, and they will be rewarded for it.