In Texas if the non custodial parent dies oweing back support does his or her kids from a current marriage have to finish paying.
Review your divorce decree, it should provide if the support obligation survives the death of the obligor. If the obligation survives, it is a debt of the estate, not of their other kids.
Please review your order. It should state what happens upon the non- custodial parents death. It is their obligation and it does not pass to someone else.