Vigorous enforcement of immigration laws, combined with a few new laws that make the general climate less hospitable to illegal aliens would solve this in short order.
We’ve already seen the proof in certain areas where this has been done. Deport 5%; 80% will self-deport. You then have the ability to deal with the remaining 10%.
Ignore my faulty math...I was dealing with generalities. I should have said 15%, though. :-P