(a) Amounts payable by the retirement system to an annuitant that are not received by that annuitant or the annuitant's bank, as determined by the retirement system, before the annuitant's death may be paid to the person named to receive benefits in the event of the annuitant's death, in accordance with rules adopted by the board of trustees. The retirement system may send a final monthly payment of an annuity to a bank or another address previously indicated by the annuitant or beneficiary.
(b) The board of trustees may adopt rules necessary to administer this section.