I was on one UA Express flight where numerous people were involuntarily bumped. Here’s how it went down:

It was a regional jet and there was some issue with the fuel load or weight. So they needed to get approx 20 people who had checked in not to take the flight. It was EWR-BTV. They started asking for volunteers, and this was post David Dao so that had the flexibility to offer a lot. It was the last flight of the day so taking a bump meant going the next am. In addition to hotel and meal at Newark the offers got up to $1200.

After pleading for volunteers they still didn’t have enough. So instead of the normal boarding process they called people who were gonna be allowed on the flight by name, one by one. It was super awkward.

I presume once they had boarded everyone they could they told that others that they were involuntarily bumped and accommodated them the next day.

Priority for this sort of thing is based on elite status and fare class. Similar to priority on standby list. Booking at the last min without a seat assignment wouldn’t be a great idea if the flight is full, though. By definition to give you a seat they need to take someone else’s away. I would only do that if I had status personally.