Yeah for people who are doing well fasting, sometimes even doing some extra exercise pushes them over the edge.
That happened to @siobhan the other day about 70 hours into a fast she decided to walk 7k and she felt, cold, then weird, and then noticed that she wasn't thinking right (I think the phrase she used was she knew she had to swipe her card at a gas station, but her brain wasn't helping her to do it).
She had some gas station cheese and salami and sat down till the feeling passed. In her case I suspect she pushed faster than her body fat could supply energy, and because after 3 days she didn't have any capacity in circulating lipids she was using it as fast as it was being released from body fat. (@DaveKeto might have an opinion on that ) In that circumstance if you want to keep going on the fast and the extra exercise is just short term, you can eat a little fat ... it may take 30 mins for that to hit your circulation so it's probably worth taking a food with a small amount of glucose ... like a Salami from a gas station
In general the first day on a fast you are using body fat AND fat being trafficked by LDL AND fat (and protein/carbs) from the food you've eaten. Second day you are now using just body fat and any fat still circulating in LDL. By day three you are running only on body fat and here's the problem for skinny people fasting. Body fat has a limit how fast it can give up energy,
If you have 20 lbs of body fat you can only release a maximum of 615 kCal/day, if you have 60 lbs you can release 1845 kCal/day. So a skinny person used to burning 1500 kCal a day all of a sudden having access to 610 kCal is probably going to feel the brakes come on.
So for that person, a little dietary fat will [ironically] help them keep in a fasted state.