Immigration law is an ever-changing subject, which you'll need to keep a sharp eye on if you're affected by it in any way. Congress often tinkers with existing immigration law (though things rarely seem to go anywhere fast), so be sure to keep yourself educated.
According to current immigration law, employers have to regularly check the paperwork for a foreign worker, and must keep it on file for three years after hire or a year after termination, whichever period is longer. Employers can't, however, be held responsible for well-forged paperwork.