Just cut them off from every government service and then weed them out . That's the way to deal with them.
If they can't cash a check, get a license, get a job, go to school, get medical care, buy a house...etc, then they are screwed and easily identified.
Once any one of those criminals gets caught, they should be deported. As it is now, normal law enforcement will not deport them or even arrest them for being illegal.