Ia a Florida case that I believe would be equally applicable in Texas, the bankrupt ex-husband was sued by his ex-wife in bankruptcy court, and the bankruptcy judge ruled that his debts for so-called "indemnification" debts, those that he had been ordered to pay in the divorce, would not be discharged as to her. Reinhardt v. Reinhardt (In re Reinhardt) (Bankr.M.D. Fla. 2012). See Section 523(a)(15) of the Bankruptcy Code.
This applies only in Chapter 7. If you file Chapter 13, and you complete your case and receive a discharge, your ex-spouse cannot try to hold you liable for these types of debts, that you were ordered to pay in your divorce decree. And as the Florida court ruled, the debts are only not discharged AS TO THE EX-SPOUSE (or spouse or child of the debtor). The creditors cannot try to collect from the debtor, their debts are discharged or canceled as to the debtor.
The only person that can collect against the debtor is the ex-spouse, and only if there was an indemnification or "hold harmless" agreement or order in the divorce decree, AND only if the ex-spouse first pays the indemnified debts. If he or she cannot pay it or doesn't pay it, or files bankruptcy themselves, then they cannot try to collect from the debtor.
Alternatively, if you think your ex-spouse may pay the debts that you were ordered to pay in the divorce decree, and then come after you to pay them, you can file Chapter 13. It depends on your circumstances but in many Chapter 13 cases, you can pay little or nothing to the unsecured creditors, so that you are getting the advantages of a Chapter 7 case. This is another good reason to file Chapter 13 instead of Chapter 7, if you have these kinds of "indemnified" debts.