There is never a time during sleep when all of the brain is sleeping - and the sleep cycle is a rotation between one part of the brain sleeping and another.
Dissociated means that some parts of the brain (and some functions) are asleep while others are awake.
In Deep Sleep the conscious mind is asleep, and we are not aware of time passing - but the muscles remain tonic, and it is possible to respond 'automatically' to the environment, tossing and turning in be, and even sleep talking and sleep walking.
In REM/ Dreaming Sleep, the muscles are by contrast paralysed, and there is no physical interaction with the sleeper's environment - but we are conscious and aware of time passing, and dreaming; and can hear and feel the environment (sometimes this gets incorporated into dreams).
Why cannot all the brain be asleep at once? Probably because we must remain in contact with the environment to some extent, and because the awake parts of the brain are needed to re-awaken those parts that are asleep.
Presumably if the whole brain is asleep and 'switched off' and out of contact with the environment; then this is a coma. And it is hard to awaken from a coma precisely because the whole brain is asleep and also cut-off from the environment so the sleeper is both paralysed and unaware - cannot hear or feel or move.
So, naturally, we are never wholly asleep.