Is it possible to sleep with your eyes open? It is generally observed that animals and human alike close their eyes when they sleep. It looks seemingly natural.

But I have heard (and might have observed one too, just not sure whether he was actually sleeping or not) that there are certain people who can fall asleep with there eyes open.

So, is it possible to sleep with your eyes open?
Nocturnal lagophthalmos is the search term you're looking for.  But it's less that they "can" fall asleep with their eyes open and more that they "can't" close their eyes during sleep:


  Nocturnal lagophthalmos is the inability to close the eyelids during
  sleep. Lagophthalmos is associated with exposure keratopathy, poor
  sleep, and persistent exposure-related symptoms. There are a variety
  of causes of lagophthalmos, grouped as proptosis/eye exposure
  etiologies and palpebral insufficiency etiologies.