A spirit death occurs when a character reaches 0 or fewer spirit points, having the last of his or her life force drained from him or her. Such a character will immediately die. However, a very quick Cleric using Preservation or someone with a white flask could still save them from decaying, if acting fast enough.
If the death results from draining spirit to exactly 0 points, the character will simply die on the spot. (Exception: if this results from use of ALCHEMY CHANNEL while at the guild training cauldrons, the character will crawl out of the training cauldron room while dying.)
However, if the death results from draining spirit to negative points, the character will die and decay immediately. This will result in significant Death's Sting penalties, and the character will be transported to the local reincarnation point (for example, in Icemule Trace's Hall of Rebirth or Wehnimer's Landing's White Altar), alive with one spirit point and reduced stats as if they had just been raised from the dead.
This fate is often the result of using Council of Light powers that consume spirit points upon their expiration carelessly, or using ALCHEMY CHANNEL while at 1 or 2 spirit points. It can also be the result of clerics, usually younger clerics, attempting Raise Dead (318) with insufficient spirit points. And it can be the result of being targeted with Living Spell (208), which can drain spirit.