Texas Civil Practice and Remedies Code - CIV PRAC & REM § 34.074. Officer's Surety

(a) An officer's surety may only be liable for the penal sum of the surety bond minus any amounts already paid out under the bond.  In no event may an officer's surety be liable for more than the penal sum of the officer's surety bond.

(b) If the officer and the officer's surety are both defendants in an action brought under this chapter, the surety may deposit in the court's registry the amount unpaid under the surety bond and the court shall determine the proper disposition of this sum or order the return of the deposit to the surety in the court's final judgment.

(c) A surety is not a necessary party to an action brought under this chapter or under Section 7.001.  Instead, a prevailing party under these provisions may bring a separate action against a surety failing to pay the amount remaining under the bond on a final judgment.  This action must be brought on or before 180 days after the date all appeals are exhausted in the underlying action.