I had an employer who did this on a regular basis. HR would hound you to sign all sorts of agreements, even going so far as to say "You have to sign this."

It was never clear what would happen if I didn't. I'm not certain you can force someone to sign a contract as a condition of employment.

My buddy came up with an ingenious solution-- we signed each other's documents in our own handwriting, so if we ever had to we could say, "That's not my handwriting."