All unpaid compensation due to a deceased employee of the state at the time of death shall be paid to the person or persons surviving at the date of death, in the following order of precedence, and the payment is a bar to recovery by any other person of amounts so paid:
(1) to the beneficiary or beneficiaries designated by the employee in writing to receive the compensation filed with Department of Administration at the time of death; if more than one beneficiary is designated, each shall share equally unless the employee specifies a different allocation or preference;
(2) if there is no beneficiary designated, to the surviving spouse;
(3) if there is no beneficiary or surviving spouse, to the employee's child or children and descendants of deceased children by representation;
(4) if none of the above, to the employee's parents, or the survivor of them;
(5) if none of the above, to the legal representative of the employee's estate, or if there is none, to the person determined to be entitled under the laws of the employee's domicile.