The soul is eternal.

“This is a very important verse in understanding the difference between the spiritual soul and the material body. The soul is eternal, as stated in Bhagavad-gita (2.20):

na jayate mriyate va kadacin nayam bhutva bhavita va na bhuyah
ajo nityah sasvato ‘yam purano na hanyate hanyamane sarire

“”For the soul there is never birth nor death. Nor, having once been, does he ever cease to be. He is
unborn, eternal, ever-existing, undying and primeval. He is not slain when the body is slain.”” The spirit soul is eternal, being freed from waste and change, which take place because of the material body. The example of a tree and its fruits and flowers is very simple and clear. A tree stands for many, many years, but with the seasonal changes its fruits and flowers undergo six transformations. The foolish theory of modern chemists that life can be produced by chemical interactions cannot be accepted as truth. The birth of a human being’s material body takes place due to a mixture of the ovum and semen, but the history of birth is that although the ovum and semen mix together after sex, there is not always pregnancy. Unless the soul enters the mixture, there is no possibility of pregnancy, but when the soul takes shelter of the mixture the body takes birth, exists, grows, transforms and dwindles, and ultimately it is vanquished. The fruits and flowers of a tree seasonally come and go, but the tree continues to stand. Similarly, the transmigrating soul accepts various bodies, which undergo six transformations, but the soul remains permanently the same (ajo nityah sasvato ‘yam purano na hanyate hanyamane sarire). The soul is eternal and ever existing, but the bodies accepted by the soul are changing. There are two kinds of soul–the Supreme Soul (the Personality of Godhead) and the individual soul (the living entity). As various bodily changes take place in the individual soul, different millenniums of creation take place in the Supreme Soul. In this regard, Madhvacarya says:

sad vikarah sarirasya na visnos tad-gatasya
ca tad-adhinam sariram ca jnatva tan mamatam tyajet

Since the body is the external feature of the soul, the soul is not dependent on the body; rather, the
body is dependent on the soul. One who understands this truth should not be very much anxious about the maintenance of his body. There is no possibility of maintaining the body permanently or eternally. Antavanta ime deha nityasyoktah saririnah. This is the statement of Bhagavad-gita (2.18). The material body is antavat (perishable), but the soul within the body is eternal (nityasyoktah saririnah). Lord Vishnu and the individual souls, who are part and parcel of Him, are both eternal. Nityo nityanam cetanas cetananam. Lord Vishnu is the chief living being, whereas the individual living entities are parts of Lord Vishnu. All the various grades of bodies–from the gigantic universal body to the small body of an ant—are perishable, but the Supersoul and the soul, being equal in quality, both exist eternally. ”

Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Seventh Canto, Chapter 07 – Text 18