Better yet, make being here illegal a felony. Then let the people make citizen's arrests.
There are some downsides to that, but it's the only way I see of ridding our society of these leaches.
We've seen far too many of them in far too little time.
Why not throw in a reward bounty? Of course, there would probably be a few gun fights, knife fights, etc., but they wouldn't involve innocents, other than the bounty seekers of course.