Whenever an employer who is a self-insurer under this chapter enters into an agreement to pay compensation to an injured employee or the employee's dependents in case of the employee's death or whenever an award is made by the Board in favor of such injured employee or the employee's dependents in case of the employee's death, the employer shall pay the full liability under the agreement or award to a savings bank or trust company in accordance with § 2359 of this title. Such fund, together with all interest arising from the investment thereof, shall be held and paid out in accordance with § 2359 of this title. Failure on the part of a self-insured employer to make such payment within 30 days after the making of an agreement or award shall forthwith terminate the right of such employer to carry the employer's own insurance.