It does not come into existence through birth, so it will not disappear with death.
It is said that the soul never comes into being and never dies. It is not something that was created at a certain time, nor did it not exist before that. It has existed since ancient times, and is described as eternal and unchanging.
In the annotations, each of the six changes that occur in the body – birth, generation, growth, change, decline, and death – is negated one by one. While the body goes through these stages, they do not apply to the soul itself. The reason why the soul does not perish even when the body is destroyed is because the soul is not a being that is born, established, grows, declines, and dies.
Japanese Translation from the Geeta Press Edition - Chapter 2, Section 20: "The soul does not come into being, nor does it die."
In the previous section, it was stated that the soul cannot be killed by anyone. Therefore, a question arises: why is the soul unable to be killed?
In order to answer this, the speaker reveals the nature of the soul while demonstrating that the soul does not depend on any change.
Sanskrit original text
न जायते म्रियते वा कदाचिन्नायं भूत्वा भविता वा न भूयः ।
अजो नित्यः शाश्वतोऽयं पुराणो न हन्यते हन्यमाने शरीरे ॥ २० ॥
Romanization
na jāyate mriyate vā kadācin nāyaṃ bhūtvā bhavitā vā na bhūyaḥ |
ajo nityaḥ śāśvato 'yaṃ purāṇo na hanyate hanyamāne śarīre || 20 ||
The soul never comes into being, and it also never ceases to be. It does not come into existence after being born. This is because it is unborn, eternal, permanent, and has existed since time immemorial. Even if the body is killed, the soul is not killed. (20)
By saying, "The soul is never born and never dies," the Lord negates two transformations: birth and death. And by doing so, he essentially negates all six transformations of the soul. Furthermore, the Lord uses other expressions to negate other transformations as well.
The six transformations are: (1) birth, (2) generation, (3) growth, (4) change, (5) decline, and (6) destruction.
By declaring the soul as "not born," the transformation of birth is negated.
The sentence "It does not exist after being born" negates the second transformation, which is "generation."
The phrase "something that has existed since ancient times" negates the third change, which is "growth." The word "constant existence" negates "change." The word "eternity" negates "decline." And the sentence "even if the body is killed, the soul will not be destroyed" negates the final change, which is "destruction."