First, it is important to agree about what sleep is. For these purposes, let’s include a lack of conscious awareness of one’s surroundings. In general, sleep involves lying in a recumbent position with the body at rest. We typically are unable to see or respond to external stimuli and we keep our eyes closed. However, as in the case of parasomnias, this may not always be the case. In these abnormal sleep behaviors, the person remains asleep, or unconscious, but is able to sleepwalk or perform other actions. They may even have their eyes open.
Some people may incompletely close their eyes during sleep, allowing the white part of the eye (called the sclera) to remain uncovered. This may occur occasionally in healthy people.
Others may be unable to close their eyes due to other medical problems. This is called lagophthalmos. It may occur most commonly as part of a condition called Bell’s palsy, which results in facial weakness and may be due to an infection of the seventh cranial nerve.
It may also be possible to disengage your mind from the processing of visual input while keeping your eyes open, such as may occur in hypnosis.
In general, sleeping with your eyes open (even if only a small degree) may be possible. It is typically harmless, but it may lead to dry or red eyes in the morning. In this case, it may be necessary to apply a lubricant to the eye and patch it overnight.