“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.