A state or county agency that sells a vessel pursuant to this part shall deposit that portion of the proceeds of the sale of the vessel that represents the mooring or other fees and charges due the agency, the expenses of the auction, and any other expense incurred by the agency in taking into custody and disposing of an abandoned vessel, derelict vessel, or vessel impounded under section 200-16, into the boating special fund or other state or county fund, as appropriate, from which the expenses incurred in connection with the vessel were paid. The balance, if any, shall be deposited into the general fund of the State. The owner may recover any balance of the proceeds from the State only if the owner files a claim therefor with the department of budget and finance within one year after the execution of the bill of sale. If no claim is made within the year allowed, the money shall become a state realization. A lien holder shall receive priority in payment from the balance of the proceeds to the extent of the lien holder’s lien on the vessel. If the proceeds of the sale are insufficient to cover the mooring and other fees and charges, the expenses of the auction, and the other expenses incurred by the agency in taking into custody and disposing of the vessel, the agency may bring an action for the deficiency in [an] environmental court of appropriate jurisdiction against the registered or documented owner or any person who had an interest in the vessel when custody was taken by the agency.