What can I legally do so that my landlord does not evict me?

They can evict you if you don't pay the rent.

Eviction is a process in Massachusetts. It will require Notice to Quit and the filing of a Summary Process for Eviction action with the Housing Court. If the landlord wins an eviction, you can file a motion for a Stay of Eviction based on your financial situation. That you are the victim of ID theft and will have the means to pay once your finances are returned to normal should go a long way with the court. You may want to develop a plan for catching up on your rent arrearage and show that to the court. You should definitely consult with a landlord-tenant attorney.

No, you have to pay your rent your rational for being broke, while unfortunate and unfair, is not a legal excuse to live rent free and breach your contract with your landlord. You will be evicted.

Unfortunately, there's not any sort of legal mechanism that can likely help you in this situation. Typically, eviction (FED) cases are pretty straightforward and are often decided one of two ways: either you can, or have, paid the rent and the landlord messed up in some way, or you didn't (or can't) pay the rent, in violation of the rental agreement. The ways in which tenants usually defeat eviction cases are often based on technical errors on the part of the landlord, such as faulty notice and service procedures, etc. Aside from that, there are other ways to win an eviction case, but they're uncommon and usually hinge on certain faulty or not-attended-to repair and maintenance issues, such as habitability violations. Given that you didn't mention anything like that in your question, I'd assume it wouldn't apply in your situation. The best case scenario in this type of situation is often to negotiate with the landlord and try to come to an agreement on getting up to date with the rental payments, etc., while staying in the rental in the meantime. Depending on when you think you might regain access to your funds, they may be inclined to listen. And letters and whatnot from individuals or organizations on your behalf relating to the ID theft may have some influence on their decision-making process. Of course, it also might have no influence at all, sadly.