One fact that is difficult for many divorcing couples to grasp is that just because something is ordered in family court does not mean third parties must adhere to it.
A common example is when a husband is absolved of making mortgage payments on a marital home in which he no longer resides. This may be forfeited in exchange for some other advantage in the divorce settlement. However, the bank is not required to adhere to this agreement - it's solely between husband and wife. So if husband's name is on the mortgage, he's technically still responsible to pay that mortgage, even if he doesn't live there and even if the family court says he isn't obligated. If the wife stops paying those mortgage payments, the husband becomes responsible for the total amount, or else the property will go into foreclosure and his credit will be dragged through the mud too.
The only recourse he would have at that point would be to sue the wife for damages under their prior agreement.