Just like God, the souls are also eternal. The soul never dies or a new is created. When a soul enters a new body, based on both good and bad action in previous births, it is assumed as the birth and when the soul departs the body, it is assumed as the death based on pure ignorance. Actually the soul simply gets attached and detached from a particular body. In Kathopanishad, 1.2.18-19, Acharya nachiketa has explained the form of soul as follows:

The meaning is that the soul is a conscious being and is neither born or dies. So the soul is neither an act of nor a reason for anything or anyone. The soul in ever present. It does not parish with the body.

A person who kills someone thinks that I am killing someone and the one who is being killed thinks that I am being killed are both ignorant, as the fact is that the soul is not destructible. In the second chapter of Bhagvat Gita, lord shri Krishna has explained this well to the Arjun. Nyaya darshan it is stated the following characteristics of the soul: These are desires, jealousy, effort, feels happiness and unhappiness and effort to acquire knowledge. Vaishashik darshan goes in even more detail. The characteristics of soul described in this darshan are: one who breaths, opens and closes eyes, is born, thinks and makes decisions, moves, has senses and body parts, gets the feeling of hunger and thirst, feels happy and unhappy, has feelings of desires, jealousy, makes efforts and works hard, These characteristics of soul and different from the characteristics of God. Only these characteristics confirm the presence of soul since the soul is nonphysical and as such cannot be seen. A living being ceases to have these characteristics once the soul leaves the body, a phenomenon called death. Just as the light is there only as long as lamp is lit and the sun is shining, life is these only as long as the soul resides in the body.

Swami Dayanand defines soul as the one who has desires, jealousy, effort, happiness, and unhappiness, knowledge which has limits and is ever present.

The soul has limited knowledge (not all knowing), stays in one place and is nonphysical and therefore the size of soul is same in all beings. Soul is free in actions, but the fruits of action are resultant of the universal laws of the supreme reality. Based on its actions, soul experiences happiness and unhappiness. After leaving the body, the next birth in a specific species, life span.

In the 7th chapter of Satyarth Prakash, Swami Dayanand has detailed this further.