Sāṅkhya Yoga · Verse 22
"वासांसि जीर्णानि यथा विहाय नवानि गृह्णाति नरोऽपराणि | तथा शरीराणि विहाय जीर्णान्यन्यानि संयाति नवानि देही"
"vāsāṃsi jīrṇāni yathā vihāya navāni gṛhṇāti naro 'parāṇi | tathā śarīrāṇi vihāya jīrṇāny anyāni saṃyāti navāni dehī"
As a man abandons worn-out garments and takes other new ones, so the embodied one abandons worn-out bodies and enters into other new ones
The most famous analogy of the Gītā. Vāsāṃsi (garments, clothes) are jīrṇāni (worn-out, worn) — the body is garment, not person. Naraḥ (man) chooses navāni (new ones) when the old no longer serve.
Dehī (the one who has a body) is the subject. Bodies are instruments, not identities. Vihāya (abandoning) is natural, not violent — simply change of vehicle.
Saṃyāti (enters, joins with) describes the process of reincarnation without drama. There is no trauma in changing bodies for one who understands; only continuity of animating principle.