I've seen this happen before, and have seen how many people missed the flight. UA usually seems to try to get them onto other carriers where possible and certainly will try to get them onto another UA flight as well.

Last time I saw this happen, I was waiting at ROA for a flight to IAD. Winds had made delayed or cancelled everything after the 6:30 am departure. The 1:00 pm, which I was on, was showing an 8:50 pm new departure time (as of 4:30 pm), and hearing that from the GA, most pax left the gate area to get dinner or to try to make one of the US, DL, or NW flights.

I was online and watching the status on United.bomb and UAL Cargo and saw it then go to a 5:00 pm departure while the GA was still announcing the 8:50 time. She hadn't even gotten the news yet! About then, though, a ramp worker opened the door and told the GA that we'd gotten a revised wheels-up window and to board immediately.

We left on a SF3 with perhaps 8 pax. The flight had originally been overbooked.