The recent controversy in the news now reminds me of two times I have been on overbooked flights. The first was United, just a one hour flight and they were asking for volunteers to give up seats. They offered $1000 and one person was a lady with a baby who needed two seats so I asked if the $1000 was cash now (or check), and if they would furnish a hotel room for me overnight. I knew they have a decent hotel, about 3 stars that their crews use, and with a short airport shuttle, so for $1000 I was willing to stay overnight and go the next morning. But turns out the $1000 was a travel voucher, so not as useful and a few other people took took the offer while I was asking.
Another time was with another airline, and plans changed at the last minute so I was the extra passenger on the later flgiht. The folks I spoke with were nice and politely said the flight was listed as full but to come to the gate from my connecting flight and they'd try to get me on. Sure enough there were a few no shows and I was the last one to get a seat about 5 minutes before departure. This happened to be in Chicago also. I hadnt eaten all day and boy that quick hot dog sure tasted good. Dont know if Chicago really has best dogs or I was just really hungry.
This last time especially they folks were very nice that made it ok, even if I had not gotten on that plane.
In both cases this was before everyone was seated on the flight and was resolves at the gate.