Probably a stupid question, but would there be any problem with just walking all day when on a prolonged fast for fat loss?
Low intensity? Basically unlimited, just get enough salt.
For fasts under ~5 days you can also do high intensity without issue, so long as you get enough salt. Eat high protein on refeeds and you shouldn’t lose any measurable amount of lean tissue. In fact you’ll probably lay down gains. HGH spikes through the ROOF on multi-day fasts, and if you eat right your IGF-1 will be through the roof afterwards.
My routine lately has been keto diet, rolling 48 hour fasts with strenuous lifting on fed days and HIIT cardio on fasted days. 200+g protien on fed days, train fasted eat after. And I’m getting my newbie gains just as well as anyone else, adding weight to the lifts every week.
Not sure how long you’re talking for “prolonged”, but I do a 40hr fast every week from Sunday night to Tuesday lunch and I run 6km Monday morning (at about the 10hr mark), 6km Tuesday morning (about 34hr in) and play a game of touch footy Monday night (about the 20hr mark) and have absolutely no problems with energy whatsoever.
In fact, if anything, the Tuesday morning run is the easiest and the Monday morning one the hardest.
If you are in good health and your body is used to fasting, there should be no issue. There have actually been studies where they had participates do just that as they wanted to monitor metabolic processes and people handled it well. IIRC, it was using a hand crank for an hour and then walking on a treadmill for eight hours.