Tex. Civil Practice and Remedies Code § 43.002: SUIT ON ACCRUED RIGHT OF ACTION.

(a) When a right of action accrues on a contract for the payment of money or performance of an act, a surety on the contract may, by written notice, require the obligee to without delay bring a suit on the contract.

(b) A surety who provides notice to an obligee under Subsection (a) is discharged from all liability on the contract if the obligee:

(1) is not under a legal disability; and

(2) does not:

(A) bring a suit on the contract during:

(i) the first term of court after receipt of the notice; or

(ii) the second term of court if good cause is shown for the delay; or

(B) prosecute the suit to judgment and execution.

Added by Acts 2007, 80th Leg., R.S., Ch. 885 (H.B. 2278), Sec. 2.11, eff. April 1, 2009.