Verify they have a legitimate Social Security number and other papers that match. When the guy the INS deported from your shop a week ago shows back up with a new name and new card --- it's a pretty good bet he's illegal --- but there's a machine shop in Michigan that did rehire someone like that ---- but they know --- most of their employees aren't speaking English at all --- that's another clue.
Sheesh. Here we go again. I'm not going to repeat again my objections to using the SS number for this purpose. I've already stated them in several of my comments above on this thread.