Specifically, my students were asking why the terms "nonliving" and "undead" are the way they are. (And why "unliving" and "nondead" seem wrong.)
"Un-" is defined as "a prefix meaning 'not,' freely used as an English formative, giving negative or opposite force in adjectives and their derivative adverbs and nouns... and less freely used in certain other nouns."
"Non-" is defined as "a prefix meaning 'not,' freely used as an English formative, usually with a simple negative force as implying mere negation or absence of something (rather than the opposite or reverse of it, as often expressed by un-)."
So "unchristian" means in some way opposed to Christian virtues, but "non-Christian" just means "not Christian." "Unprofessional" means not up to professional standards of behavior (not showing up for appointments, say), but "nonprofessional" just means not in a profession.
Logically, then, "non-dead" might mean something like "not having died" (true of rocks and living people), and "undead" might mean "living." But word constructions don't always make sense. "Non-dead" isn't a word and "undead" means non-living and supernaturally animated. Go figure.
Nonliving is more like not intended to be alive than something which is not alive. Undead is surely alive but it is more towards dead than alive - say If somebody is suffering from illness, you can say he's living undead. In more of negative way You can say he is undead in accident (positively - survived an accident)