Generally speaking the CS remains due to the named parent and all the remedies and sanctions remain in effect --but I suspect the local judge won't toss him in jail as quickly for contempt if the person tobe supported is no longer a child in need. .
However in some states there is a time limit on how long you can snooze before the debts turn legally stale
Yes, the estate should owe the debt if not otherwsie legally stale but if you fail to present a prompt claim against the estate then by operation of estate law your claim quickly becomes stale
You cannot squeeze blood out of a stone --but unless EX is truly destitute and w/o any means to pay I suggest you crank up your collection efforts
I suspect DE law governs as to when your ability to collect from a DE resident turns stale but I simply don't know.