(a) The health insurance coverage of any employee and his dependents, if any, shall cease upon the discontinuance of his term of office or employment, subject to rules and regulations which may be prescribed by the Board for extension of coverage and for conversion to an individual contract providing for such of the benefits provided under this subchapter as may be provided under such individual contracts, under terms approved by the Board, the total cost of any such contract to be borne by the employee.
(b) In the event of death of an employee having coverage at the time of death for himself and his dependents, and where the circumstances of death are such that beneficiaries or dependents of such deceased employee are entitled to an accidental death benefit payable by the retirement system on account of death resulting from an accident sustained in the performance of his duties or to death benefits provided for under the workers' compensation administration law, the unremarried spouse of such employee covered at the time of his death and his covered dependents, for so long as they would otherwise qualify as dependents eligible for coverage under the rules and regulations of the Board, shall be eligible to continue full coverage under the health insurance plan upon payment at intervals determined by the Board of the full cost of such coverage. The Board shall adopt such rules and regulations as may be required to carry out the provisions of this subsection which shall include, but need not be limited to, provisions for filing application for continued coverage, including reasonable time limits therefor, and provisions for continued coverage of spouse and dependents pending determination for an application for accidental death benefits from the retirement system or pending determination of a claim for death benefits under the workmen's compensation law.