In my experience reputable hotels will usually be supportive when this arises and try to find a solution that works. Depending on no-show rates, the percentage of non-guaranteed bookings, and other variables they may decide to just extend the stay and see what happens. If the hotel is expecting to be full with confirmed reservations and there is no other option but to decline the extension then the hotel will usually be able to find alternative accommodation nearby through their industry contacts.
I have only come across a couple of instances in 30+ years working in the industry where there was absolutely no availability in the city but usually people are aware of this and adjust their schedules/flights.