By state law in MA you can be evicted for non-payment of rent, violating the lease terms and failure to cure the violation after being given notice of the violation and a reasonable time to cure the violation, or so that the landlord can retake possession of the unit at expiration of the lease if you refuse to leave. A tenant at will must vacate with 30 days written notice spanning one full rental period. The landlord can commence eviction proceedings if the tenant refuses to leave.
In the dead of winter, the judge presiding at the eviction hearing *may* give a tenant with small children a little extra time to move before being evicted forcibly by the county sheriff. That's at the judge's discretion but won't be six months and will not be rent-free regardless of how much additional time the judge allows.
Some local communities may have more restrictive eviction rules. Cambridge is notorious for being excessively "tenant friendly" but this has tended to drive rents sky high to compensate. Cambridge may also allow squatters to remain for an unreasonably long period of time if the landlord has violated any of the rules on evictions, but will order them to pay rent while the case is pending. It can also be notoriously difficult for a landlord to recover simple possession (as long as rent is being paid) unless they are going to place a family member in the rental unit. And tenants can fight what they deem to be "excessive" rent increases even in apartments that are not rent controlled. Tenants can also fight change of use, such as reconversion of a large multi-unit home back to single-family configuration.