Soul is infinite, omnipresent, i.e, it is present in our body and outside our body.
Complete Works of Swami Vivekananda [Volume 2/Jnana-Yoga/The-Atman] :-
It is the Atman, beyond all, the Infinite, beyond the known, beyond the knowable; in and through That we see the universe. It is the only Reality. It is this table; It is the audience before me; It is the wall; It is everything, minus the name and form. Take away the form of the table, take away the name; what remains is It.
People say the seat of soul is in the heart of beings. How is that even possible? By restricting it to a particular location, we are making it finite and soul is infinite.
Astavakra Samhita I.19:
Just as a mirror exists within and without the image reflected in it, so the Supreme Self exists inside and outside this body.
Krishna says in the Bhagavad Gita:
aham ātmā guḍākeśa
aham ādiś ca madhyaṁ ca
bhūtānām anta eva ca (10.20)
Meaning- I am the Supersoul, O Arjuna, seated in the hearts of all living entities. I am the beginning, the middle and the end of all beings.
When people die, we say that their soul has passed, which under any case cannot happen because there is not a place where a soul can go because it exists everywhere. Atman cannot have any "hole" in it, it must exist everywhere at all the times.
When a person dies, soul should still be present in their bodies. So what exactly makes a person die?