Does this sound like a realistic case to get sued over (and lose)?

In this book I'm writing, the main character runs some kind of factory, and he loses a lot of money because he was sued by one of his employees over an injury. I was thinking that the employee either tripped over a wire and broke something, or general inattentiveness caused his hand to get cut off.

hmm... not if there was a counter measure of this signed onto the agreement of working there.

If you want, you could have a comically assholish union trying to bleed the main character dry.

^^ In worker liability laws, cutting your own hand off via incompetence or operator negligence does not result in the employer being liable. Tripping over a wire can be a liability to the employer under certain conditions like excessive slack in a walkway (and not covered by a mat for instance).

What if the employee lied about what happened?

This might sound really horrible, but I think it might help if...er...the area it took place in was...not the slums.

^^^ If the employee is found lying he's subject to criminal prosecution for fraud in many jurisdictions.

It depends on the venue and the lawyers involved, but an injured employee can sue for negligence and win. You have to prove that the employer knew about a dangerous condition in the plant and failed to correct it in a timely manner. Forcing the employee to sign an agreement doesn't necessarily absolve the employer of all blame, and in fact can make it look like the firm has something to hide.

The same principle applies to individuals. If you know about a loose board on your front porch but don't fix it, someone can get hurt and sue you.