No memory, just continuing reveries. I suspect this may be due to alternating influences from the right and left halves of the brain. Even if that is not what happens, the eyes still move. EMDR may come close enough to imitating those eye movements that the work of dreams can be done while the patient is awake. Since the patient is already awake, the dream does not have to end.
Memory is left where once there was only reverie.
Now the sleeper may sleep, and not be frightened from sleep by horrid nightmares. Healing has happened. Just a theory, you understand.