LET THEM STAY! but tax the mess out of them because you can't just come to the land of the free and expect to get in for free ..
At least this way the taxes will be used to help pay for their healthcare education as well as the foreigners tax and taxes taken from their now legal jobs. I think the more we try to push them away the more resources we are actually having to use to keep them out and the more under the table and non taxed money will be evading our economy.
As far as being deported for crimes, I still believe that ALL and I repeat ALL people regardless of race be sentenced to the service and maintenance of all public goods for free to repay us for all the tax money we use to keep them locked up. If they have to be a burden to both society and my wallet then the people should get some sort of benefit out of their stay. This is not taking away their freedom, but this is helping both society and the criminal see what it's like to do good and see others like themselves helping out, kinda like a re-entry to society program