Tex. Gov't Code § 2257.113

Enforcement of a penalty imposed under Section 2257.107, 2257.108, or 2257.109 may be stayed during the time the order is under judicial review if the participating institution pays the penalty to the clerk of the court or files a supersedeas bond with the court in the amount of the penalty. A participating institution that cannot afford to pay the penalty or file the bond may stay the enforcement by filing an affidavit in the manner required by the Texas Rules of Civil Procedure for a party who cannot afford to file security for costs, subject to the right of the comptroller to contest the affidavit as provided by those rules.