There is a fundamental disagreement among some Advaita Vedantis as to what becomes of the jIva in suShupti. Bhagavatapada Shankaracharya says in bhAshya on Brahma Sutra 1.iv.18 so: "The general vedanta doctrine says that the jIva becomes one with the highest brahman in suShupti". Mandukyopanishat says the same thing by using words such as praj~nAnaghana or Gaudapadacharya's explanation of Anandaghana to the jIva becoming one with brahman. To my understanding, the people who object to this have turiyA as a separate fourth state in their mind, in contrast to the three states of waking (jAgRta), dream (svapna) and deep sleep (suShupti). However, turiyA is not really a state or the fourth quarter in Mandukyopanishat, but its that which makes the avasthAtraya One Whole, being in all the three states. That is, it remains in all three states as the substratum.
Lets rephrase that last statement and see that it means: brahman remains in all three states as the substratum. Bhagavatapada says in his most famous quotation "jIvo brahmaiva nA'parAH". Having made that statement, why is it then that suShupti gains a special focus in his Brihad bhAshya? Well, to understand that, we have to look into Mandukya kArikA and recall Bhagavatapada's introductory note of Brahma Sutra Bhashya (BSB). In the kArikA 11, Gaudapadacharya explains prAj~na (jIva in suShupti) to be conditioned by cause alone, not effect, while viSva (jIva in jAgRta) and taijasa (jIva in svapna) are conditioned by both cause and effect. The cause here is avidyA of one's own nature. The effect is jIva _as_an_individual_ in the waking or dream worlds. In the introduction part of BSB, Bhagavatapada says that this (effect of) jIvatva, as an individual, is naisargika. Strictly speaking, that is exactly what makes a jIva. What else is a jIva without individuality? This has already been shown to have been mentioned as jIvo brahmaiva nA'parAH. So suShupti being the case of jIva having no individuality, there is no jIvatva there to qualify the effective separation from brahman, and hence its so-quoted _becoming_one_with_brahman_. This is the reason why Mandukya mantra 5 calls prAj~na as praj~nAnaghana, a mass of consciousness and mantra 6 goes further to completion by saying that it is from him that all beings originate, being sarveSvara, the source of all.
However, there still remains a separate question as to what is that cause which prAj~na gets conditioned by? That is avidya, in seed form. Without this remaining, there would be no waking up from the deep sleep state for jIva. He would realize then and there. Even while being brahman in deep sleep, he doesn't know that he is brahman owing to this ignorance. Contrast this with avidyA in jAgRta and svapnAvasthA-s, which is not in seed form, but a full-blown tree, with jIvatva making a separate individual existence for jIva. jIva as viSva and taijasa, both, considers himself as an individual. The objectors ask as to how would prAj~na be one with brahman, while avidyA remains even in seed form? The answer to that is: just the way that brahman remains unaffected as brahman during pralayA, while holding avidyA of all the jIvas in seed form (for next cycle of creation). Else, if such a seed remains outside of brahman, that would go against a-dvaita itself and become dvaita!