I said “serfs” because I saw no reason to think the Church might have owned slaves during the Roman Empire, but its status as a medieval landlord raises the possibility of serfs.
Which also gives us the name of our ten-cent piece.
No, whoever owns the factory owns the workers. Except not, as you say.
If there were such things as factory-serfs bound legally for life to that factory, then whoever owns the factory owns the workers.