B.G 2.20

na jāyatē mriyatē vā kadācin nāyaṁ bhūtvā bhavitā vā na bhūyaḥ । ajō nityaḥ śāśvatō’yaṁ purāṇō na hanyatē hanyamānē śarīrē ॥ 2-20॥

The Lord is neither born nor does he die. The ever existent neither come into being nor ceases to exist. The Jīva transmigrating from one body to another is unborn, eternal, and permanent (as he is similar to Lord). The Jīva is not destroyed when his body is destroyed.

Gīta Bhāshya 2.20

Lord is eternal and the same always. Jīva is eternal, as he is similar to the Lord. But, he has a variance in knowledge, unlike the Lord. As Jīva travels from one body to another, he is called ‘purāna’.

atra mantravarṇō’pyastītyāha– na jāyata iti॥ nacēśvarajñānavad bhūtvā bhavitā। taddhi - ‘tadaikṣata’ (chāṁ.u.6.2.3)

‘dēśataḥ kālatō yō'sāvavasthātaḥ svatō'nyataḥ। aviluptāvabōdhātmā' (bhāga.3.7.5)

ityādi śrutismr̥tisiddham।

Even the Vedic hymns accept that the being is unborn. But unlike the knowledge of the Lord, knowledge of the being undergoes variations. It is so stated in ‘tadaikshata’ Vedic statement (chāṁ.u.6.2.3).

“In all places and time, in all states, without there being a difference in its nature or form, Lord with his knowledge is the same.” - bhāga.3.7.5

So he is famous in Vēdas and Purānas.

kutaḥ? ajādilakṣaṇēśvarasarūpatvāt। śāśvataḥ sadaikarūpaḥ। puraṁ dēham aṇatīti purāṇaḥ। tathā’pi na hanyatē hanyamānē’pi dēhē ॥20 ॥

How is Jīva eternal? Because of its similarity with eternality and other qualities of the Lord. Eternally Lord has a single unchanging form. Jīva is called 'purāna' as he travels from one 'pura', body, to the other. Therefore, even when the body is destroyed, it does not cease to exist.

Gīta Tātparya 2.20

There are two references to 'unborn' and 'permanent' in the above verse. So, one refers to the Lord, and the other to the Jīva. Else there will be a redundancy error. The word 'Purāna' refers to transmigrating Jīva. Scriptures state Jīva to be permanent, and thus the dependent nature of Jīva is also permanent.

jīvēśvarayōḥ nityatvē mantravarṇōpyastītyāha - najāyatē mriyatē iti। ayaṁ nā paramapuruṣaḥ bhūtvā vidyamāna ēva dēhasambandha rūpēṇāpi bhavitā na। maraṇaṁ tu dēhaviyōga iti siddhamēva। na hi ghaṭādīnāṁ maraṇavyavahāraḥ। svarūpānāśaḥ kaimutyēnaiva siddhaḥ।

There is scriptural evidence as well to prove the eternality of the Lord and Jīva. So it is stated 'najāyate mriyate'. 'nāyam bhūtva' - means the Parama-purusha, the supreme being, exists at all times. 'bhavita nā' - denies any relation (of the Lord) to the physical body. Death is well known as separation from the body. Insentient objects like pot do not have a transactional relationship related to death. Destruction of such insentient forms is certainly not spoken in terms of death.

ayaṁ jīvōSpi ajaḥ nityaśca। anyathā punaruktēḥ। śāśvataśca। na kadācidasvātantryādikaṁ jīvasvarūpaṁ jahāti। alpaśaktirasārvajñyam pāratantryamapūrṇatā। upajīvakatvaṁ jīvatvamīśatvaṁ tadviparyayaḥ। svābhāvikaṁ tayōrētat nānyathā syāt kathañcana। vadanti śāśvatāvētāvata ēva mahājanāḥ॥ iti mahāviṣṇupurāṇē। purāṇi aṇati gacchatīti purāṇaḥ ॥20 ॥

The words 'ajah' i.e. unborn and 'nitya'i.e. everlasting, refer to Jīva, the being. Else it is repetition and results in redundancy error. The Jīva is said to be 'shāshvata', i.e. permanent. So, the dependent attribute of Jīva is natural and a permanent character that does not change with time.

“Limited power, limited knowledge, dependence, incompleteness, and being a subsistence being are Jīva’s natural qualities. To be a living being, i.e. to be Jīva, is the opposite of being the 'Īswara', which means the Lord. Hence, the wise declare the Jīva to be eternal.” - stated thus in Mahā Vishnu Purāna.

As Jīva obtains various bodies, he is called 'Purāna'