According to Hindu scriptures, there is no death for the Atman (soul is a wrong term). The human Atman (jīvātma) is considered to be of the same essence as the Divine Supreme Atman (paramātma), also termed as Consciousness. Hence the Atman, in the Hindu context, is eternal, imperishable, changeless, and that which illumines everything.
The Atman can be thought of as a source of light. While the furniture in a room might keep changing, the reason one can see and experience these items is due to the presence of the light. Similarly, we are able to perceive, feel and think in the world because of our soul.
Lord Krishna declares in the Bhagavad Gita, Chapter 2, Verse 20:
na jāyate mriyate vā kadāchin nāyaṁ bhūtvā bhavitā vā na bhūyaḥ
ajo nityaḥ śhāśhvato ’yaṁ purāṇo na hanyate hanyamāne śharīre
The Atman is neither born, nor does it ever die; nor having once existed, does it ever cease to be. It is without birth, eternal, immortal, and ageless. The Atman is not destroyed when the body is destroyed.
Thus, Hindu theologians conclude that the Atman does not die. When a person passes on, their body decays, mind stops thinking, but the Atman, however, continues to exist. It leaves the body and moves onto a different realm of experience, based on what that particular Atman needs for evolution. This is valid for all living beings, and not just humans. It is due to this belief system that Hindus propound the theory of karma and reincarnation. The Atman evolves by taking on different births, until it reaches spiritual maturity and finally merges with the Divine Consciousness. This, liberation (moksha), is the goal of life on earth.
Other reading material: Reincarnation: WHO is it that Travels? Atma? Jiva? Subtle body?
Relevant videos: Swami Nikhil Anand Hinduism Q & A: What happens when we die?, Hinduism Q & A: Can the soul die?, Hinduism Q & A: What is Reincarnation?,
Contributor: Lakshmi Subramanian
Location of this post (16b): https://www.hinduspeakers.org/ufaqs/can-the-soul-die/