back child support payer deceased

My father passed away almost one year ago and he still owed my mother 10,000
in back child support. I am 24 now, before he passed my mom was still
recieving back child support. Since he has paid into social security all
these years shouldnt she still be able to collect? When he passed away he
had nothing. Is this something that just goes away after the payer dies?
Also when he died he was in Texas and the child support was owed from the
state of California.

His estate should pay that off if any assets existed.