Personally I doubt a large percentage of illegals are self employed sub contractor's by any normally accepted definition. But I'll play, where are their FICA remittances? Only difference in your scenario, they're breaking the tax laws rather than their employer.
Since it is illegal to be here to start with, what makes you think the care about the tax law.
A few day's ago some Texas contractor came by my house, he was clearing the gas line for Duke Utilities, three 80,000 dollar tractors, all driven by Mexicans., I'd say if you ask duke utilities they would say it was a contractor sub contracted to a sub contractor, etc, etc.