N.Y. Comp. Codes R. & Regs. tit. 2 § 345.5
This option provides payments to the member for life. Upon the member's death a retirement allowance in an amount equal to one-half of the amount of the allowance paid to the member shall be paid for Life to such person as he shall nominate by written designation duly acknowledged and filed with the retirement system at the time of retirement. Under this option a member may not change his beneficiary after the close of the period provided by section 90 of the Retirement and Social Security Law for the making of an election. Upon the death, prior to the death of the member, of said person so nominated, the member shall, commencing with the payment for the next following calendar month, begin receiving, in lieu of the allowance then payable, an allowance equal in amount to that which would have been payable if no optional modification of the retirement allowance were in effect. This option shall not be available where the actuarial equivalent of the amount(s) which the pensioner may receive is less than fifty percent of the actuarial equivalent of the retirement allowance without optional modification.
N.Y. Comp. Codes R. & Regs. Tit. 2 § 345.5