On my first day in Utah the estimable Ali Miller took me through Keyhole, the Zion equivalent of Grand [I guess to check me out

After having done most of the abseils and swims, and as the canyon opened out, Ali and I heard someone bellowing ‘help’. At the final big drop we found a middle-aged couple with little gear and less experience, the woman hanging half way down the 90ft (27m) rappel with her abseil gear jammed. She had been there for nearly an hour.
We managed to lower her to the ground by setting up a top belay and just cutting her original rope. She was in shock, but fortunately we were carrying an emergency bivy to keep her warm and plenty of food and water. Ali went off to get the park rescue service, who turned out to be on their way already, as someone had heard the cries for help from the road.
It was two hours before the paramedics got there, and we were the last people down the canyon that evening (avoiding the heat), so this incident might easily not have ended so well.
The man had done a couple of commercial guided trips, the woman none, and they had just decided to give it a go -- they went out that morning and bought two harnesses, an ATC and one biner each, and a massive 11mm rope ("we thought it would be safer").
We think the issue was just a kink in the rope that stuck in the ATC, but this was someone not very physical, quite overweight, and with no capacity to use brute force to get themselves free. They had no other equipment with them and were wearing shorts and T-shirts with no extra warm clothing.
As well as the emergency bivvy, this rescue cost me a beanie and Ali a spray-jacket -- we needed everything possible to keep the casualty warm and these went out with her.