B.G 2.20

न जायते म्रियते वा कदाचिन् नायं भूत्वा भविता वा न भूयः । अजो नित्यः शाश्वतोऽयं पुराणो न हन्यते हन्यमाने शरीरे ॥ २-२०॥

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’.

अत्र मन्त्रवर्णोऽप्यस्तीत्याह– न जायत इति॥ नचेश्वरज्ञानवद् भूत्वा भविता। तद्धि -‘तदैक्षत’ (छां.उ.६.२.३)।

‘देशतः कालतो योऽसाववस्थातः स्वतोऽन्यतः। अविलुप्तावबोधात्मा’ (भाग.३.७.५)

इत्यादि श्रुतिस्मृतिसिद्धम्।

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.

कुतः? अजादिलक्षणेश्वरसरूपत्वात्। शाश्वतः सदैकरूपः। पुरं देहम् अणतीति पुराणः। तथाऽपि न हन्यते हन्यमानेऽपि देहे ॥२० ॥

G.B 2.20.2

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.

जीवेश्वरयोः नित्यत्वे मन्त्रवर्णोप्यस्तीत्याह - नजायते म्रियते इति। अयं ना परमपुरुषः भूत्वा विद्यमान एव देहसम्बन्ध रूपेणापि भविता न। मरणं तु देहवियोग इति सिद्धमेव। न हि घटादीनां मरणव्यवहारः। स्वरूपानाशः कैमुत्येनैव सिद्धः।

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.

अयं जीवोSपि अजः नित्यश्च। अन्यथा पुनरुक्तेः। शाश्वतश्च। न कदाचिदस्वातन्त्र्यादिकं जीवस्वरूपं जहाति।

अल्पशक्तिरसार्वज्ञ्यम् पारतन्त्र्यमपूर्णता। उपजीवकत्वं जीवत्वमीशत्वं तद्विपर्ययः। स्वाभाविकं तयोरेतत् नान्यथा स्यात् कथञ्चन। वदन्ति शाश्वतावेतावत एव महाजनाः॥ इति महाविष्णुपुराणे।

पुराणि अणति गच्छतीति पुराणः ॥२० ॥

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'