The most important thing you would look at is whether either of them have another residence; if not, that is a good start. Other things would be where their mail is directed, if they are registered to vote there; if their car is registered there, etc.
Evaluating any legal question requires a detailed knowledge of the specific facts involved. A short question will rarely contain all the relevant facts. Therefore, the answer here should be considered a general comment for your consideration and not legal advice. It does not create an attorney-client relationship.
First of all, if there is an alimony order in place your ex would have to file with the court for termination of alimony through a complaint for modification based on your cohabitation. He cannot simply discontinue alimony simply because he thinks he has grounds. The court will determine if there is cohabitation (must be 3 months or more) based on the evidence your ex provides. Proving cohabitation is difficult, however, and very fact specific. Generally the court will look for economic and social integration of the cohabitants – are they living together as a familial unit or just as roommates. That is, do they share a bedroom, are they legal residents of the same household, do they have joint banking accounts or credit cards, do they own property together, do they have reciprocal wills or insurance policies, etc.?
This is not legal advice and is not intended to create an attorney-client relationship. You should speak to an attorney for further information.
Massachusetts General Laws chapter 208, section 49 defines cohabitation. I have attached a link to the statute. Generally speaking, cohabitation means living in the same household for a period of 3 continuous months with a significant other. Evidence of cohabitation includes economic interdependence of the couple, having a reputation in the public as a couple, as well as other factors.
Cohabitation is typically proven in a number of ways. One is having a private investigator follow the former spouse to prove that he/she is cohabiting with another person. Another is obtaining financial records to prove that the couple's finance are commingled.
If you currently have an order to receive alimony, your ex cannot unilaterally stop paying alimony. He will need to file a Complaint for Modification to suspend, reduce, or terminate alimony, pursuant to the Alimony Reform Act. If you do not yet have an order of alimony, the issue of cohabitation will have to be addressed when negotiating alimony.
NOTE: This answer is for informational purposes only. By responding to this question, this attorney’s answer does not create an attorney/client relationship with the person posing this question, and there is no attorney client privilege between you and the attorney responding. The answers provided are based upon the facts presented. Since many cases are very fact-specific, any person posing questions on this site should consider consulting with an attorney to discuss his/her case in greater detail to provide a more thorough and detailed analysis of the question posed. This site should not be used as a substitute for competent legal advice from a licensed professional attorney in your area who regularly practices in the subject matter which your question is about. The law changes frequently and varies from jurisdiction to jurisdiction.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.