Hmmmm, now where have I read of this happening before? Oh yeah! The Soviet Union right after the Bolshevik revolution and the beginning of the "workers paradise". Of course the housing problems in Stalin's USSR started going away as the gulags filled up.

A few observations:

1) The majority of the people of the area are now receiving exactly what they voted for. I don't feel sorry for those voters at all !!
2) This could be an opportunity for commie liberals to embrace the ultimate virtue signal of the open border mantra [ARE YOU LISTENING MARTHA'S VINEYARD?].
3) Now the governor of Massholechusetts and the mayor of Boston and faculty and some students of Harvard academia can show us all how it's done and lead the way by opening their homes first. They must answer how many unvetted illegals are coming to stay for dinner at their houses?

Before you get the knock on your door, time to fill your house with poor relatives

I would think that a federal lawsuit, invoking a "creative" interpretation of the 3rd Amendment, might be in order, should any government (federal, state, local) try a stunt like this.
Some up-and-coming lawyer could "make his bones" with a case like that.

I'll take one if she will absolutely veto any new firearm legislation.

Certainly anyone that chooses can house and illegal border crossed. But since crossing illegally is a crime, would that be considered harboring a criminal?

Illegal aliens planted in MY house wouldnt want to be there, I guarantee tht.

A political “request” will generally lead to compulsion. This can be protected by the Third Amendments as the new migrants will be the foot soldiers of the Statists

We have housed homeless people at our place a few times. Every time we wound up paying for it. Last one cost several thousand stolen from us and neighbors. An earlier one worked with us to establish a legit business, but managed to run it tens of thousands or more into a hole. We never knew how much we lost. (If you steal repeatedly from someone, also steal their financial records because that'll delay the consequences. Stuff gone, but no proof.)

Back up in Massachusetts, decades ago, a friend found a job for a really nice and polite street person. Job started Monday, but Tuesday she was back on the street. "Couldn't do that job. They wanted me to come in at nine every morning!"

Over in the early days of the thankfully deceased Soviet Union the government placed extra people into your too-large house. Maybe six families in eight rooms with one bathroom.

A friend in Massachusetts has 16 horses. Maybe she'll choose to house some of those families in her stable. "You'll sleep in this stall with old Pooples." "But won't he poop on me?"

Massholes.
Couldn't happen to a more deserving state.
I worked there for the better part of 50 years, as that was where the high tech jobs were.
I left five years ago, and not a moment too soon.