Does the state owe my husband money for his employment?

Your Husband should check the policy(ies) related to this matter.

I can not answer your question, because it is not a question about the law. Such matters are governed by the rules of the agency. I suggest your husband go and ask them. Some employers, including states, pay un-used vacation, some do not. Some only pay when the employee is separated. Some forfeit if not taken, some forfeit every year, some forfeit if discharged. Some pay upon request. There is no one law that governs. Therefore, no one answer. Human Resources will know the answer.