If the dwarf is a "hero" ("master" or "lord" in their military title, bright colored face), then they may continue as if on the "active/training" schedule even when you put the squad on "inactive", because "hero" dwarves were intended to never leave the military, and never perform any civilian duties ever again.
Of course, it's horribly bugged, so dwarves typically (but not always) lose hero status at the beginning of every month, but I suspect "hero"s hanging around after the orders are cancelled is mostly due to that, when I switch a squad of marksdwarves from "active/training" (with "patrol route" assigned as their schedule), the ones that are currently labeled as "hero"s tend to hang around for an extra month, while the rest go back to their civilian duties right away.
Some of it could be because switching to "hero" status wiped out all of their labors, so they don't have any job to get to, but it's at least possible that your dwarf is hanging around despite being hungry/thirsty because dwarves on "station", "patrol route", "defend burrows" (and the like) won't drink or go eat until they hit starving or dehydrated.
If you change the squad's schedule to have them training, and give them a barracks, I'll bet your dwarf will go get something to eat/drink more quickly, because military dwarves that are training don't wait until they're starving/dehydrated.