Can't speak for Smithfield, but LOTS of companies hire LOTS of illegal workers, not always intentionally. It's remarkably easy to be fooled by fakey-doo papers, and unless someone "cracks down", you might NOT know.
Then again, plenty of businesses could care less: the money they save offsets whatever puny fines they may have to pay if they are busted. Some companies are infamous.
I know of communities of people who share social security numbers; it takes a while to get caught, in which time you could put away some money and take care of yourself and your family for a while.
Not surprisingly, an employee on thin ice is not likely to complain about working conditions.
The flip side of all of this is that there are not (in my opinion) enough people who are willing to do these kinds of jobs that many Hispanics, especially Mexicans, both legal AND illegal, are doing now. As many of our immigrant ancestors did, they work like dogs, don't (for the most part) make trouble or ask questions. They are grateful for the work, however hard, dangerous and insecure it might be.
It is a big and complicated issue not easily solved or even tackled by the kind of knee-jerk legislation we've seen in recent years.