The living body is dead, it stopped working. Its either buried, burned or left to a normal decomposition process.
To change from a living to a non-living, the soul has to release itself from the body.

Now how does a soul know when to release itself?
In fact the soul does not know anything.

In case of accidental death, one of the vital organs stops working or there is a massive loss of fluid called the blood.
When the damage is irreparable, the soul gets the indication that now its the time to leave.
In case of natural death, the soul knowing the condition of the body knows that the time to leave is coming soon.
In case of near-death, where the body is revived by artificial or natural means, I think what happens is once the body"s vital organs start failing,
the soul prepares to leave, but it somehow knows that the person is not completely dead.

All the vital organs do not stop working at the same time. So if in  some way the body is revived, the soul continues to be there.

Where does the soul stay?
If continuing with the proposition that all living things have a soul, now where does it stay?
Taking an example of a plant.
If I cut one branch, its still alive. So soul is definitely not in one branch.
If I cut some part of the bark, still the tree is alive.
If I uproot a tree, it dies but if I implant a seedling from one soil to another its still alive.
So a body takes some time to die and only after that time the soul leaves.
As for the location of the soul, I am satisfied with Heisenberg"s uncertainity principle.
Roughly saying that at any point of time, the soul can be anywhere in the body.
I may place it close to the heart or the brain but its not very important to me.

After the living body is completely dead, the soul comes out of the body
and is either destroyed instantaneously or goes back to the higher power (as per its origin).
If the soul goes back to the higher power then there is a full chance of it getting recycled or what we call as rebirth.