Only the temporary material bodily vessel the individual jiva-souls are contained in, within the material world are born and eventually come to an end. The individual jiva-souls are just one living entity in a category with other living entities known as the "life force" headed by Krsna, the Supreme Personality of Godhead and cause of all causes. In the material world, the outer material bodily vessel covering the individual jiva-souls, eventually decays and fades away and merges back into the "oneness" of lifeless material energy.

The eternal individual jiva-soul (anti-matter) then moves on to another temporary material body.

The jiva-souls (marginal living entities) are unique anti-matter living entities, or individual beings as a eternal spiritual bodily form, are beginningless and endless like Krsna, therefore indestructible.

Because of choosing mistaken desires that lead us to continue rejecting Krsna, the individual jiva-souls are continually forced to remain trapped in the temporary material energy.

However, the individual jiva-souls always remain eternal whether they are in the spiritual world or material world.  

Therefore, the eternal indestructible individual jiva-souls have to continue acquiring material bodily containers or vessels. This is called the repeated painful cycle of birth and death.

Bhagavad Gita As It Is - “Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be.” (BG, Ch 2 text 12)

Bhagavad Gita As It Is - “As the embodied soul continuously passes, in this body, from boyhood to youth to old age, the soul similarly passes into another body at death. A sober person is not bewildered by such a change." (BG, Ch 2 text 13)

Bhagavad Gita As It Is - “Those who are seers of the truth have concluded that of the nonexistent [the material body] there is no endurance and of the eternal [the soul] there is no change. This they have concluded by studying the nature of both." (BG, Ch 2 text 16)

Bhagavad Gita As It Is - “That which pervades the entire body you should know to be indestructible. No one is able to destroy that imperishable soul." (BG, Ch 2 text 17)

Bhagavad Gita As It Is - “The material body of the indestructible, immeasurable and eternal living entity is sure to come to an end; therefore, fight, O descendant of Bharata." (BG, Ch 2 text 18)

Bhagavad Gita As It Is - “Neither he who thinks the living entity the slayer nor he who thinks it slain is in knowledge, for the self slays not nor is slain." (BG, Ch 2 text 19)

Bhagavad Gita As It Is - "For the soul there is neither birth nor death at any time. He has not come into being, does not come into being, and will not come into being. He is unborn, eternal, ever-existing and primeval. He is not slain when the body is slain." (BG, Ch 2 text 20 "corrected" 1983 edition)

Bhagavad Gita As It Is - "As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones." (BG, Ch 2 text 22)

Bhagavad Gita As It Is - "The soul can never be cut to pieces by any weapon, nor burned by fire, nor moistened by water, nor withered by the wind." (BG, Ch 2 text 23)

Bhagavad Gita As It Is - "This individual soul is unbreakable and insoluble, and can be neither burned nor dried. He is everlasting, present everywhere, unchangeable, immovable and eternally the same." (BG, Ch 2 text 24)

Bhagavad Gita As It Is - "One who has taken his birth is sure to die, and after death one is sure to take birth again. Therefore, in the unavoidable discharge of your duty, you should not lament." (BG, Ch 2 text 27)

Bhagavad Gita As It Is - "Some look on the soul as amazing, some describe him as amazing, and some hear of him as amazing, while others, even after hearing about him, cannot understand him at all." (BG, Ch 2 text 29)

Bhagavad Gita As It Is - "O descendant of Bharata, he who dwells in the material body can never be slain. Therefore, you need not grieve for any living being." (BG, Ch 2 text 30)

All individual jīva-souls are eternal persons, therefore there are no new jiva-souls ever being created because they have always existed, meaning they are beginningless and endless like Krsna. 

Even though Kṛṣṇa the Supreme Lord is ultimately the maintainer of both the material world and the spiritual world and not a blade of grass can move without first being sanctioned by Him.

Srila Prabhupada – "There are no new souls, new and old are due to this material body, but the jiva-soul is never born and never dies, so if there is no birth, how can there be new souls?" (Letter to Jagadisa dasa 9th July 1970)

The individual jiva-souls therefore are eternal spiritual living PERSONS and can never be destroyed, terminated or extinguished because the jiva-souls are indestructible.×**×.