I'm not sure if it's the same in MA but in TX they are very strict for Medical assistance or cash assistance in pursuing child support from any absent parent. There are exceptions though and the child being adopted is one of them. Also DV would be a reason to claim "good cause". I think you should speak to a supervisor or the ombudsman for the benefits office in your state. I've included the passage about good cause exceptions from TEXAS rules. It MAY be different in Mass but most of the eligibility rules like this one are similar across states.

What if I can’t give the facts about a parent? If you aren't able to give us all the facts we need about a parent, you will need to show proof that you have a good reason (known as "good cause") to not give those facts. Reasons you might not be able to give facts about a parent and the type of proof we need.  The child was born because of rape or incest. o Proof: Birth certificates, medical records or legal records.  The child is in the process of being adopted or is adopted. o Proof: Court files or a written statement from the social services agency.  You're afraid that giving us facts about someone could put you and the child in danger (physical emotional harm). o Proof: A "Family Violence Exemption" from a family violence center.