Bhagavad Gita, Chapter 2, Verse 20

This is never born, nor does it die. It is not that, not having been, it again comes into being. This is unborn, eternal, changeless, ever itself. It is not killed when the body is killed.

The soul was never born, so it never dies. The body ends. It doesn't.

Being born, growing, aging and dying all happen to the body. None of it happens to the soul.