In the 2nd ed Book of Lairs (collection of short quests) the Crimson Death one is set by a vampire-

he remembers his soul leaving his body- he heard a voice telling him that he could become human again by getting his soul back- and once his sire was dead, he did the research, and found out what his soul had become (a monster called a Crimson Death) and eventually, where it was.

So he hires The Party to retrieve it.

So you can have a soulless undead, which nonetheless has volition, and a desire to change its condition.