My perception is somewhat different from what you ask.
Just like people say their heart is broken, or full of love, we know love is in fact not at all involved with the heart. It is a brain function. It is the brain’s individual reaction to perception of events and environment.
So in the same context, I would assert that a soul does not exist in a segment form, but is the term given to the aspects of conscious thought and personality traits of a given individual. Hence, when the brain dies, the person ceases to exist.
On another note, the belief in NDEs and post death knowledge can be explained by the lack of knowledge which exists about human brains. I believe it is possible that medical equipment may be not capable of fully detecting brain activity. It may be humans have been aware of their surroundings beyond a perceived cessation of brain activity because medical personnel and equipment were unable to recognize a lingering brain activity.
This is supported in a small way by people “returning to life” after only a short time.
Anyway, in regards to the question of soul, I do believe that is a term applied to the functions of the brain which define individual personality.
If I’m wrong, then I hope good souls continue to exist after the death of their host bodies.