Texas Election Code - ELEC § 31.037. Suspension or Termination of Employment

(a) The employment of the county elections administrator may be suspended, with or without pay, or terminated at any time for good and sufficient cause on the four-fifths vote of the county election commission and approval of that action by a majority vote of the commissioners court.

(b) In a county with a population of more than 4 million, the secretary of state may enter a written order to terminate the employment of a county elections administrator at the conclusion of administrative oversight of the county elections administrator's office under Subchapter A if the recurring pattern of problems with election administration or voter registration is not rectified or continues to impede the free exercise of a citizen's voting rights in the county.