If they had souls, the souls would be spiritual, they would not be susceptible to disaggregation and would be immortal.
Is it possible to consider this extraordinary faculty as a disaggregation?
disaggregation dis·ag·gre·ga·tion (dĭs-āg'rĭ-gā'shən)n.
A breaking up into component parts.
An inability to coordinate various sensations and a failure to observe their mutual relations.