With that said: by breaking the contract with Dr. Dao, it would seem that United is therefore required to pay up the cost of Dr. Dao's ticket.
It isn't too hard to come up with a situation where passengers are already boarded, but then are forced off the plane. (Ex: weather conditions change. Another airliner crashes in the runway, causing an unknown amount of delay, etc. etc.). Surely under such a situation, all the "already boarded" passengers will be forced off the plane, and probably refunded the full value of their ticket.
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But under no circumstances is there actually a requirement to fly every passenger. I'd expect that the absolute limit that can be forced onto United Airlines is the ~$1350 cash + Refunded Plane Ticket.
Well, aside from the broken nose and concussion. But that's the Chicago Police's problem, not United.