Well like, in the Torchwood spinoff from Dr. Who, they had two people like you say. The first was Jack Harkness, who couldn't die ever, and he was basically just immortal. The second was this other random character who "died" and was brought back as "dead". He was still walking about happily, but his body couldn't heal or otherwise do much.

Technically, you could take either of these characters, separate them into jars, and then they would be less than functional. I think that our zombies are a cross of these two kinds of things, where we can "kill" them by separating them into bits or otherwise ruining their flesh, except for when the totem is nearby to bring them back. Other undead would follow this same idea.