That illegal immigration almost requires ID theft is obvious. But here: https://www.city-journal.org/html/illegal-more-ways-one-13089.html
If the Internal Revenue Service hasn't notified you that your identity has been stolen, that doesn't mean it wasn't..…www.rt.com
Also, while immigrants as a whole have a relatively low crime rate, that isn’t necessarily the case for illegal immigrants. First, some huge proportion of them commit identity theft and employment fraud. And, their victims are disproportionately legal immigrants.
As to violent crimes, discussion here: http://immigration.procon.org/view.answers.php?questionID=000782
Note that those who argue that illegal immigrants aren’t associated with higher crime rates leverage the decreasing crime rate overall, not illegal alien criminals vs citizens and legal immigrants.