Jīva is said to be eternal since he owned up doer-ship and its result which makes him continue to live from one body to another one, therefore why should we afraid of death? Lord Krsna explained what is happening during the time of death of this physical body in next verse,
manaḥṣaṣṭhānīndriyāṇi prakṛtisthāni karṣati ||15.7||
śarīraṁ yadavāpnoti yaccāpyutkrāmatīśvaraḥ | gṛhītvaitāni saṁyāti vāyurgandhānivāśayāt ||15.8||
And when the one who rules (the body) departs, he draws to himself the five senses and the mind, the sixth, obtaining in the body. When he obtains a new body, he goes, taking these (sense organs and the mind) with him just as the wind (would carry) the fragrance from their sources (the flower).
When jīva leaves the body, he draws - karṣati the five senses, mind and intellect - manaḥṣaṣṭhānīndriyāṇi, which exist in prakrti (the physical body) - prakṛtisthāni together with him. Each sense organ abides in its own place in the body and operates when the jīva is alive. Then, at the time of death, each one leaves the respective place where it once functioned, and now no longer function as it did. This jīva who is a kartā and bhoktā due to ignorance, although he is really of the nature of param brahman, now leaves this body behind and travels in certain subtle form.
śrotraṁ cakṣuḥ sparśanaṁ ca rasanaṁ ghrāṇameva ca | adhiṣṭhāya manaścāyaṁ viṣayānupasevate ||15.9||
Presiding over the ear, the eye, the senses of touch, taste, and smell, and the mind, this person (jīva) experiences the sense object.
The conscious being is presiding over / occupies / pervading the sense organs - adhiṣṭhāya. Because of I-ness and mine-ness he takes the subtle senses as him and when he assumes another body, he enjoys the sense objects again with all the sense organs, because he must have the means to enjoy the sense objects, due to attachment.
utkrāmantaṁ sthitaṁ vāpi bhuñjānaṁ vā guṇānvitam | vimūḍhā nānupaśyanti paśyanti jñānacakṣusaḥ ||15.10||
The deluded do not see the one who is departing (from the body) or even remaining (in the body), experiencing or endowed with the guṇas. Those who have the eye of wisdom, see.
nānupaśyanti - they do not see in keeping with the śāstra. Even though śāstra says “you are brahman”, due to lack of discrimination, they are deluded - vimūḍhā. Shankara says that ātmā who is available in every cognition, being self-evident behind every sense organ and the mind, is not seen due to delusion in the form of lack of discrimination. The lack of capacity to discriminate is due to the strength of love and attachment for seen and unseen enjoyments. On the other hand, there are people who see the nature of themselves clearly through the eye of wisdom - jñānacakṣusaḥ.