The estate of any prisoner transferred pursuant to § 40.1-5.3-7 to the facility provided for in § 40.1-5.3-1 shall be liable for the expense of his or her care and treatment therein. At the request of the fiscal agent of behavioral healthcare, developmental disabilities and hospitals, the general treasurer, on behalf of the state, shall commence and prosecute to final judgment and execution any necessary and proper action, suit, or proceeding at law or in equity, against the estate of the prisoner for the collection of such expense.