Something I wonder about as a 20-30x/year pax to whom this has only happened to me a couple of times.
Let's say you get to the airport and the plane is cancelled for some technical issue. That's, say, a full A320 or B737 with 180+ pax. Last time this happened to me at LGW with Air France (20:00 or so), the airline offered me overnight accommodation and a place on the first flight out the next day from LHR. I had quite a nice room at the LHR Hilton.
But now I wonder... wasn't that plane the next day also mostly fully booked already? There were 4 or 5 AF planes a day from London to Paris at the time. Unless they all had 20% spare capacity, how is everyone going to get out the next day? Do some cancel (maybe those who were going to a 9am meeting in Paris and so there was no point in travelling)? Do some accept extra compensation and wait longer?
And the bonus question: Same thing, but the airport is closed for 6 hours due to bad weather, or there's an ATC issue, and a hundred flights are lost. Where does the capacity come from to get those 20,000 people to their destinations? Is there a pool of planes and crews set aside for this sort of thing, or do those 20,000 have to get squeezed into an assortment of flights with a couple of free seats each?
I'm interested in anything that someone with experience in these cases might be able to disclose. And let me add that you must have one of the worst jobs in the world, having to deal with frustrated/angry/screaming pax...