The Jiva dwells in Brahman during deep sleep.. In this section of his Brahma Sutra Bhashya, Adi Shankaracharya says that even though the Upanishads speak of the Jiva dwelling in the veins or pericardium during deep sleep, those are just the means by which it comes to dwell in Brahman:
'The absence of that,' i.e. the absence of dreams--which absence constitutes the essence of deep sleep-takes place 'in the nâdîs and in the Self;' i.e. in deep sleep the soul goes into both together, not optionally into either.--How is this known?--'From scripture.'--Scripture says of all those things, the nâdîs, &c., that they are the place of deep sleep; and those statements we must combine into one, as the hypothesis of option would involve partial refutation.... That again the nâdîs and the pericardium have to be combined as places of deep sleep appears from their being mentioned together in one sentence ('Through them he moves forth and rests in the purîtat). That that which is (sat) and the intelligent Self (prâgña) are only names of Brahman is well known; hence scripture mentions only three places of deep sleep, viz. the nâdîs, the pericardium, and Brahman. Among these three again Brahman alone is the lasting place of deep sleep; the nâdîs and the pericardium are mere roads leading to it. Moreover (to explain further the difference of the manner in which the soul, in deep sleep, enters into the nâdîs, the pericardium and Brahman respectively), the nâdîs and the pericardium are (in deep sleep) merely the abode of the limiting adjuncts of the soul; in them the soul's organs abide.
Nor do we finally maintain that the nâdîs, the pericardium, and Brahman are to be added to each other as being equally places of deep sleep. For by the knowledge that the nâdîs and the pericardium are places of sleep, nothing is gained, as scripture teaches neither that some special fruit is connected with that knowledge nor that it is the subordinate member of some work, &c., connected with certain results. We, on the other hand, do want to prove that that Brahman is the lasting abode of the soul in the state of deep sleep; that is a knowledge which has its own uses, viz. the ascertainment of Brahman being the Self of the soul, and the ascertainment of the soul being essentially non-connected with the worlds that appear in the waking and in the dreaming state. Hence the Self alone is the place of deep sleep.
Ramanujacharya says the same thing in this section of his Sri Bhashya:
Next the state of deep dreamless sleep is enquired into. Scripture says, 'When a man is asleep, reposing and at perfect rest, so that he sees no dream, then he lies asleep in those nâdîs' (Kh. Up. VIII, 6, 3); 'When he is in profound sleep and is conscious of nothing, there are seventy-two thousand veins called hita which from the heart spread through the pericardium. Through them he moves forth and rests in the pericardium' (Bri. Up. II, 1, 19). 'When a man sleeps here, he becomes united with the True' (Kh. Up. VI, 8, 1). These texts declare the veins, the pericardium, and Brahman to be the place of deep sleep; and hence there is a doubt whether each of them in turns, or all of them together, are that place. There is an option between them, since they are not in mutual dependence, and since the sleeping soul cannot at the same time be in several places!--To this the Sûtra replies--the absence of dreams, i.e. deep sleep takes place in the veins, in the pericardium, and in the highest Self together; since these three are declared by Scripture. When different alternatives may be combined, on the ground of there being different effects in each case, it is improper to assume an option which implies sublation of some of the alternatives. And in the present case such combination is possible, the veins and the pericardium holding the position of a mansion, as it were, and a couch within the mansion, while Brahman is the pillow, as it were. Thus Brahman alone is the immediate resting-place of the sleeping soul.
Madhvacharya also says the same thing in this excerpt from his Brahma Sutra Bhashya:
The state of sleep which is the absence of wakefulness and dreams, is brought about within the Lord present within the Nadis. For the scriptural passages say "Then (in sleep) in these Nadis (in the Sushumna), the soul is come (Ch. VIII. 6. 3) "O dear one, during the state of sleep, this person (soul) comes to be with Sat (the supreme Lord)" (Ch. VI. 8. 1).
And for good measure, this excerpt from Srikantha Shivacharya's commentary, this excerpt from Baladeva Vidyabhushana's commentary, and this excerpt from Nimbarka's commentary also say the same thing. This seems to be a rare case of unanimous agreement among all commentators on the Brahma Sutras! (I discuss other such cases here, here, and here.)
By the way, Adhyaya 3 Pada 2 of the Brahma Sutras also discusses two related issues: first, that the same soul which went to sleep wakes up from sleep in the same body, and second, that fainting is a state that's like half-way between deep sleep and death.