Upon receipt of a written application filed with the board by a designated beneficiary, the board shall grant a death payment to the designated beneficiary of any member who dies:
(1) while in service;
(2) while a recipient of a disability retirement benefit, if the benefit has been in effect less than 6 months;
(3) while disabled, if the member has been continuously disabled since discontinuance of the member's service but is not receiving a disability retirement benefit; or
(4) while an inactive member.