“Un-” is a negative prefix denoting the opposite of the word to which it is affixed. The nearest equivalent prefix is “non-”, which denotes the same thing. “Un-”, however, also possesses a connotation (in many applications of the prefix) of time, where previously the state or thing that is not, once was.
In the case of zombies, the term “undead” is used to refer to them as a collective whole, as a race or species. “Nondead” is less appropriate, for while it would convey the fact that zombies are far more ambulatory than the normative deceased, it fails to convey that the zombies were once dead; or, if it does convey that, it does so with much less force.
(Another example of this connotation, although one based in marketing rather than in organic etymology, holds for “uncola”; 7up has always been a carbonated sweet water, and therefore a cola, although it subverts the usual formulae for what is deemed as cola, and in so doing is perceived [due to intensive advertising more than anything] as having progressed from a state of being cola to a state of being beyond cola.)
The utility of the “un-” prefix used in this manner cannot be overstated. For clearly, the undead, while no longer deceased, also are no longer living. The simple addition of this prefix drums up a word for a third state of being.