In Dark Sun there’s virtually no mention of souls (perhaps in fact none), but in Denning and Abbey there’s essence, that which goes to the Gray upon death.
Obsidian spheres in Mind Lords of the Last Sea, aka guardians, as well as the crystals in The Darkness Before the Dawn, show how minds can continue existing inside objects, after body death.
I assume essence isn’t transferred. A guardian isn’t a ring of mind shielding or a gem of Amara; you can’t be resurrected by an outside party. I assume it’s like it is for the undead - their mind is intact despite their essence having moved on to the Gray or having been consumed in the process of turning.
Sounds like a guardian contains…a copy of a mind.
For the sake of storytelling it is safer to consider the copying process as destroying the original mind, meaning a living person cannot be copied more than once, and by extension undead cannot be copied.
Now can this copied mind…be copied? Out of one guardian, can you make many?