Tex. R. Civ. P. 153
As amended through February 20, 2024
When an executor or administrator shall be a party to any suit, whether as plaintiff or as defendant, and shall die or cease to be such executor or administrator, the suit may be continued by or against the person succeeding him in the administration, or by or against the heirs, upon like proceedings being had as provided in the two preceding rules, or the suit may be dismissed, as provided in Rule 151.
Tex. R. Civ. P. 153