>There is a tremendous exposure to legal risk both for the contracting company and the company that hires the contracting company if they employ workers who do not have the right to work in the US.

That's why you layer it so the people taking the risk are little more than hourly employees themselves.

Big corp hire cleaning corp to clean. Cleaning corp hires local cleaner to clean. Local cleaner hires legal worker with plenty of contacts who aren't legal, gives them the cash to get the job done with what ever 'contractors' they want. While local cleaner could technically be found guilty, they'll always through the local legal employee under the bus and rarely ever get prosecuted. At worst they'll be shut down and then they'll just open up under another name. Cleaning corp is effectively immune and can always find a new local cleaner if the previous one is shut down. Big corp might not ever know what is going on, they are just paying someone who handles things for cheaper than directly employing the cleaners (at least cheaper on certain budget reports that they needed to make look better).