Bankruptcy discharges the debtor's personal liability on, among other things, outstanding attorney fees. If the agreement does not have a contingency wherein you are to pay the fees, then you cannot be sued for the fees.
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If he says he's filing bankruptcy, that doesn't mean he's really going to do it. He might be bluffing. Whether bankruptcy helps him depends partly on how he is in non-compliance. Is he behind on child support? If he is, the attorneys fees to enforce the child support would also be child support--and bankruptcy wouldn't help him. He'd still have to pay.
Domestic support obligations are not dischargable in bankruptcy. Any provision of your divorce decree or your settlement agreement (as approved by the court in your divorce proceedings) that sets forth you and your ex-spouse's financial obligations to each other will survive a bankruptcy proceeding. You will receive a notice from the bankruptcy court if he does file bankruptcy. At that time the notice from the bankruptcy court will tell you important deadlines for asserting your rights in his bankruptcy proceedings.
The Bankruptcy Code provides broad protections to ex-spouses from deadbeats who are attempting to get out of their obligations by declaring bankruptcy. Even court-ordered attorney's fees may be covered. Keep all documentation concerning the judgments against him and retain a bankruptcy attorney to object to any attempted discharge of his obligations to you if/when he files for bankruptcy.
The information provided here should not be taken as a substitute for legal advice from retained local counsel. Mr. Basmaji does not intend to create nor does he consent to a formation of an attorney-client relationship with anybody, including the question poster, just by virtue of posting information on this website. If you are in need of legal advice, you should consult and retain local legal counsel.