Completely random. It depends on the HR of that company. And huge corporations have different HR depts with their own policies in different branches.
Most "legit" firms will ask you to provide documentations and proofs that you are allowed to work so more than just SSN is needed. Some companies have a don't ask don't tell policy.
Best way is to just ask their HR about it. Ask if they are willing to give u a paycut in return for paying under the table. That usually gets the implied message across.
Try the smaller shops. Retail, from my, experience tends to be harder to get into than the restaurant/food service world. But give it a try. I love retail myself. I'd gladly work at a crappy panties shop any day over a taco place.
