Where would they have gone? They're right there.
Discussion
That assumes one continuous consciousness is bound to the body.
True, but when I wake up in the morning I remember before I fell asleep, and I remember my dreams. There are obviously periods of my sleep when I don't have any memories, but before and after those periods I seem to have a consistent sense of self. If there was some other consciousness, I don't when it would be active.
Maybe your brain reconstructs your identity when you wake up but your other consciousness is gone elsewhere. You feel continuous because the brain loaded the data it stored of you from long term memory (think hard drive) but the new instance of you is not in any shape related to the one that was there before you fell asleep.