Can my ex-husband claim a child he no longer supports as a dependent?

During our divorce, my ex-husband and I divided up our children as far as who will claim them as dependents, even though they all live with me. My now 20 year old daughter is one of his listed dependents. She is a full time college student, but he does not support her in any way except for health insurance. All of her expenses are paid by herself or me (her mother). I am not trying to claim her, we are just trying to determine if she can file without being a dependent this year. Thank you.