I have a dumb question but how often do tourist visa overstayers get deported while running their own business under an incorporated ITIN? There's not even an I-9 check for non-employee income. There's got to be millions of people doing something like this or as 'independent contractors' considering how trivial it is and the obvious completely broken immigration system that demands these kinds of hacks.
Why would you go through the trouble? Most people I worked with in restaurants would just find someone’s name/ssn to use, put they had 10 children, and never ever file taxes. I think there was a shady underground way to match illegal immigrants with SSNs. Or they just networked heavily in their communities.
Many 'illegal immigrants' also entered legally with a visa that allows them to get a real SSN, like most J1 exchange scholars or students. These cards usually show a line saying not for work except for permission, but there is probably an underground network for faking a normal one.