To add a bit to this discussion, I am linking an old thread (which, in turn, links another even older one) that touches upon some of these issues. I certainly am not doing this to discourage discussion, but rather to add more ammunition.
http://forum.barrowdowns.com/showthr...ght=necromancy
I agree that Gollum and the Nazgul were not "dead," however the Nazgul may be where Gollum would have ended up, after being "stretched too thin." Then again, this may not be true because Gollum no longer had the Ring (but of course the Nine were "held" by Sauron so maybe the Wraiths didn't "have" their Rings). Nor was Gollum "undead." But the Nazgul, notwithstanding JRRT's characterization?
The Dead of Dunharrow were, obviously dead, as was Gorlim. How their shades remain, considering the Doom of Men, is an open question.
When we reach the Barrow-Wights, we touch upon the Necromancy thread linked above. Maybe a correct description would be dead but inhabited?
I hope that this encourages some more brainstorming.