Rotten is a relative term.
Up this way many found dead animals were eaten up and too relatively recently, meat taken from, well carrion
, was know as "Branx", usually venison or mutton. With the intestines in; meat spoils very quickly, but it spoils from the inside out. Shoulder, neck and haunches are all removable without disturbing the membranes containing the innards.
Depending on the temperature, how much sun the corpse is exposed to etc, the condition of the corpse when found, all has a bearing on usability, as does the constitution of the end user, it's all relative.
Me, I've never eaten any Branxy meat, but I have had a few haunches off road killed deer that I didn't hit myself. Some of the older generation of crofter and hill worker/labourer, shepherds/ghillies etc ate Branxy meat they found routinely, and according to the stories some of it was pretty ripe. In Iain Thomson's book, "Isolation Shepherd" there's a funny story about a Tramp who bunks down for a couple of nights out in an isolated spot, in order to repay his hosts he cooks up some venison. The Tramp was fine but both the hosts got ill after the meal. Turns out the Tramp had taken the venison from a bloated deer carcass he found floating by the shore of a nearby loch.
In my time there were still older folks who would (and it's likely still going on) hanging a beast (deer) in a shed, off a tree behind the house etc, and cut meat off as it was required, and some of it was allowed to get very ripe and maggoty whilst still being used, a month wasn't unknown, just cut the outer rotten meat off to get to the better stuff below. Subsequent modern shop dependent generations may wax a little squeamish at the thought, but the non vegetarians consumers will happily munch 28 day old hung beef. The only difference being the controlled environment that modern shop meat is stored.
Hunger is a great leveler, 24 hours after your last helping of beans on toast and almost all of us would be turning our noses up at carrion, wined the clock forwards by another 72 hours with still nothing to eat and no prospect of finding a wendy's coop tesco wallmart etc and the culinary part of the brain will be whirring with the possibilities afforded by bits of that same corpse.