When an order for the payment of compensation for personal injury or death is made under this chapter, the board, upon payment of the amount of the order, is subrogated to the cause of action of the applicant against the person responsible for the injury or death and is entitled to bring an action against the person for the amount of the damages sustained by the applicant. If an amount greater than that paid under the order is recovered and collected in the action, the board shall pay the balance to the applicant.