(a) In the event of the death of a member of the fund who is in good standing and who has not commenced receiving any benefits under this chapter, the designated beneficiary of such deceased member shall be entitled to be paid the amount of $5,000.00, upon making proper application to the secretary-treasurer of the fund. Such application shall be accompanied by a certified copy of the death certificate of the deceased member and such other information as may be required by the board.

(b) In the event of the death of a member of the fund who is in good standing and who has commenced receiving benefits under this chapter, but who has not received total benefits in an amount equal to $5,000.00, the member's named beneficiary shall be entitled to receive the difference between $5,000.00 and the amount of benefits received by such deceased member, upon making application as provided for in subsection (a) of this Code section.