HELP! Can the estate of deceased custodial parent sue for back and future child support from deadbeat dad?

This must be a very difficult for the children, although who do the children want to live with? Here's the deal, just because the mother is deceased, doesn't erase his debt. Also, back child support has no bearing on the fact that he is these children's father and with that being said, it is the same as far as the relationship with the kids, just because he is their father, doesn't mean the courts are going to find him to be the right custodial guardian. IF THEY GUY HASN'T PAID CHILD SUPPORT IN 8 YEARS--I don't think he is miraculously going to begin paying it now. I would plan on zero financial support if you are choosing to raise the children, additionally I believe any funds from back child support would go to the children, not the guardian.