In case of the death of a conservator who has not made a final settlement of his or her conservatorship and when there shall have not been granted letters of administration or testamentary on his or her estate, the sureties on his or her official bond may proceed to make settlement of his or her administration of the estate as conservator in the probate court having jurisdiction thereof by filing an account and vouchers for final settlement with the succeeding conservator or cestui que trust or minors and guardian ad litem where minors are interested.