The problem is easy to solve if all states followed it.
1. Criminalize business owners that hire illegals
2. Make obtaining a drivers license, a home, utilities, bank account very hard
3. Tax the hell out of money sending shops (in turn they will tax the hell out of the money senders)
4. Restrict government assistance to none legally documented immigrants (make exceptions for Asylum refugees, Permanent Residents)
Problem solved
Some of that has taken place in GA and a few other states and thus far the immigration of Mexicans alone has dropped by more than 40% in the last 5 years.