Hi Diana
First, look at your court order (if you have one) as that may address the issue. If the court order does not address the issue, then it would be necessary to check the Mass. laws. I am not a licensed attorney in Massachusetts so I cannot answer the question, however in some states, the ex can make a motion to modify an order requiring him or her to pay health insurance if the former spouse remarries.
You can search the internet typing in "remarriage", "health insurance" and "Massachusetts" and see if you can find a site that will answer your question. There are also resources in states to assist with legal issues. Check with your local state bar association and see if they can direct you to a resource. I hope this helps. Good luck.