(a) An employee of a participating municipality is included within the coverage of the supplemental death benefit program on the first day of the first month in which:
(1) the employing municipality is participating in the supplemental death benefits fund for coverage of all members it employs;
(2) the employee is a member of the retirement system; and
(3) the employee is required to make a contribution to the retirement system.
(b) Once established, coverage of a person in the supplemental death benefit program continues until the last day of a month in which a requirement of Subsection (a) is not met.