Dunno - doesn't sound legal. Not even ethical, if you ask me.
The right and honorable thing, is for them to be deported upon contact with US law enforcement. And for all the billions of dollars that the IRS is illegally refunding to these people, we could have fully barricaded the southern border by now.
They need to go home and fix the root problems in their own countries that compelled them to escape here in the first place. If we bar the door, perhaps they'll find the courage to do so.
The problem with deportation upon contact with law enforcement is the punishment for murder/rape/theft/robbery/assault/child molestation is then decreased to deportation.
I am leaning towards a non-government solution. No allocated funds can be expended toward research or punishment of crimes committed against illegal aliens.