Security deposited in compliance with the requirements of this chapter shall be placed by the director in the custody of the State Treasurer and shall be applicable only to the payment of a judgment or judgments rendered against the person or persons on whose behalf the deposit was made, for damages arising out of the accident in question in an action at law, begun not later than the period of time provided in Section 6-2-38(l), with regard to actions for injury to the person or rights of another not arising from contract, or any successor statute of limitations, for general negligence, following the date of such accident or within the period of time following the date of deposit of any security under subdivision (3) of Section 32-7-8, or to the payment in settlement agreed to by the depositor of a claim or claims arising out of such accident. Such deposit or any balance thereof shall be returned to the depositor or his or her personal representative when evidence satisfactory to the director has been filed with him or her that there has been a release from liability, or a final adjudication of nonliability, or a duly acknowledged agreement, in accordance with subdivision (4) of Section 32-7-7, or whenever, after the expiration of the period of time following the date of the accident or from the date of any security under subdivision (3) of Section 32-7-8, the director shall be given reasonable evidence that there is no such action pending and no judgment rendered in such action left unpaid.