In an old thread, which I forgot to tag, there was a similar discussion. What I ended up with after participating in that thread is:
Body = physical form, represented by Str and Dex. Manifested critters use thier Wis and Int in the place of the missing stats.
Life Force = animus, represented by Con. Unnatural life force is represented by a lack of Con.. and often has a set of conditional reponses, as in skeletons.
Mind = intelligence and memory, represented by INT. This is the portion of the critter that 'speak with dead' interacts with.
Soul = supernatual portion, represented by Wis, XP, and alignment. Loss of a Soul reduced the Wis to 1, changed alignment to TN, and the critter cannot earn XP.
character = B + L + M + S
Construct = B + L + S(*)
Mindless Undead = B + L + S(**)
Intelligent Undead = B +L (**) + M + S (*#)
(* Constructs and Animated Objects use partially formed Elemental souls. The result is a neutral alignment and incapability to gain XP.)
(**either positive or negative dependant on how it is created. The magical alteration corrupts the Body and traps the Soul, meaning that Raise Dead and similar spells will not work and the Soul cannot continue its journey. The enforced inactivity will eventually wither away the Souls earned XP. As long as the Mind and Soul are not transformed, Resurrection or Reincarnation still work, but only after the unnatural Life Force has been destroyed.)
(*# Due to the corruption of the Life Force, the Soul transforms, becoming single natured similar to an Outsider. The Mind also is transformed in such a way that it cannot be recovered, not even by True Reincarnation.)
The remaining Stat, CHR, is a combination of the Mind and Soul. Loss of the Mind makes CHR rather pointless, but a character can still interact without a Soul. One additional penalty to the loss of a soul is that your CHR is considered to be a ‘10’ for the purposes of interaction with others. Some animating magic fills in the blank when Mind or Soul is missing or not fully formed by installing an artificial CHR of 1
I prefer this interpretation as it ties the fluff to crunch. A demon's deal to take your soul *means* something.
YMMV