If a former member who is eligible for a vested allowance dies before payment of the vested allowance starts, the Board of Trustees, after receiving proof of death, shall pay the former member’s accumulated contributions to: the designated beneficiary; or if there is no designated beneficiary, the former member’s estate. If a former member who is not eligible for a vested allowance dies before withdrawing the former member’s accumulated contributions, the Board of Trustees, after receiving proof of death, shall pay the former member’s accumulated contributions to: the designated beneficiary; or if there is no designated beneficiary, the former member’s estate.