Source? I've heard of companies hiring undocumented workers, but that's not the same as knowingly hiring them, or failing to do checks. For instance, the workers could have used stolen/forged SSNs.
At least in construction related industries, it's an open secret that tons of the workers are illegally working. Even if companies do the bare minimum required by law to check for work documents, they do it once and never think about it again. Smaller companies will sometimes just pay in cash off the books.