Deadbeat dads often threaten to file bankruptcy (or actually do declare bankruptcy) in order to be absolved of paying child support. But in actuality, he cannot discharge any child support obligations simply by declaring. In other words, child support will still remain owing, regardless if he files for bankruptcy or not.
Any moneys owing for back child support cannot be discharged (cancelled) in any bankreptcy proceedings. If he owes the money prior to bankruptcy, he will still owe the money after bankruptcy.
A deadbeat dad can not escape any obligations for back child support, so threatening you with bankruptcy is simply an empty threat (or a real thread on his part, but he has not been informed that he will still owe all child support owing).