It happens all the time. The most common thing they do is this - if you have a hundred shares of Apple and you tell them you're going to just hold it forever and not worry about the short term swings, they write calls or puts for their own account using your shares - that accounts for a large percentage pf their trading profits. It's like having an affair...everyone's doing it but no one ever talks about it.
If I am going to sell 1 put I may as well work as a cashier in Walmart. I sell always 5-10 and a few times a year more. Always monthlys expirations. Its like they delay quotes or something otherwise I would short the stock just before the market close. Then the next morning when I got put stock it opens down so I dump it for a loss. I'm not holding a sinking stock. Bad enough I have to find ok trades now I have to trade against my broker?