What's keeping them in the city? JOBS! They could stay in Mexico and be jobless. They stay here because here is where the jobs are.
What draws them to the city? The assurance that they won't be deported.
No reason to stay if no one is hiring.
True, except for a few things you're conveniently forgetting like no fear of deportation, free education, free health care, driver's licenses, welfare benefits, you know, stuff like that.
Make it so social services has to turn them in if they don't have legal citizenship.
If you show up at the ER with a bullet wound, they have to call the cops. Make it so they have to turn in someone who doesn't have insurance. If they are legal citizens no biggy but if they don't have ACA because they aren't here legally, then they are obligated to call the cops.
But they could just be mexicans visiting here. What documentation do you take when you go to Canada or Mexico. What if they have a passport?
How do they get past the DMV?