Tex. Est. Code § 403.057

Except as otherwise provided by Section 16.062, Civil Practice and Remedies Code, the running of the statute of limitations shall be tolled only by a written approval of a claim signed by an independent executor, a pleading filed in a suit pending at the time of the decedent's death, or a suit brought by the creditor against the independent executor. In particular, the presentation of a statement or claim, or a notice with respect to a claim, to an independent executor does not toll the running of the statute of limitations with respect to that claim.