Modern medicine determines death by neurological criteria, but various religious groups may have reservations. For example, orthodox Jews require all vital functions to fail and do not consider a patient breathing on a respirator as dead. What is the Hindu physiological criterion of death?
Physiological criterion of death is provided in Shreemad Bhagvat Purana (Canto 3 Chapter 31 Verse 44 & 45) The answer is given by "sage Kapila" , Who is proponent of "Sankhya Philosophy". The topic of this chapter in which it's describe is - SB 3.31: Lord Kapila’s Instructions on the Movements of the Living Entities.See Here
जीवो ह्यस्यानुगो देहो भुतेन्द्रिय मनोमय:।
तन्निरोधोsस्य मरणमाविर्भावस्तु सम्भव॥44॥
jīvo hy asyānugo deho bhūtendriya-mano-mayaḥ tan-nirodho ’sya maraṇam āvirbhāvas tu sambhavaḥ
Meaning - In this way the living entity gets a suitable body with a material mind and senses, according to his fruitive activities. When the reaction of his particular activity comes to an end, that end is called death, and when a particular type of reaction begins, that beginning is called birth. SB 3.31.44
And the exact and Precise criterion of death is given in next verse
द्रव्योपलब्धिस्थानस्य द्रव्येक्षायोग्यता यदा।
dravyopalabdhi-sthānasya dravyekṣāyogyatā yadā
tat pañcatvam ahaṁ-mānād utpattir dravya-darśanam
Meaning - When the eyes lose their power to see color or form due to morbid affliction of the optic nerve, the sense of sight becomes deadened. The living entity, who is the seer of both the eyes and the sight, loses his power of vision. In the same way, when the physical body, the place where perception of objects occurs, is rendered incapable of perceiving, that is known as death.SB 3.31.45
Here what Sage Kaplia telling us is , "The subtle body ,mind and various body parts (Indtiya, इंद्रिय) remains attached until a jiva attain moksha or liberation.This gross body is a place where jiva(soul) experiences material pleasures.Both this Gross & subtle bodies when gets united its called Birth and When these gross and subtle bodies stops working in unity then its called death.