(a) If a candidate files a withdrawal request after the deadline prescribed by Section 145.092, and the candidate complies with each requirement under Section 145.001 except that the candidate's filing to withdraw is untimely, the authority responsible for preparing the ballots may choose to omit the candidate from the ballot if at the time the candidate files the withdrawal request:
(1) the ballots have not been prepared; and
(2) if using a voting system to which Chapter 129 applies, public notice of the test of logic and accuracy has not been published.
(b) If a candidate dies on or before the deadline for filing an application for a place on the ballot:
(1) the authority responsible for preparing the ballots may choose to omit the candidate from the ballot; and
(2) if the authority omits the candidate's name under Subdivision (1), the filing deadline for an application for a place on the ballot for the office sought by the candidate is extended until the fifth day after the filing deadline.