Why do people sleep with their eyes open?
The medical term is "lagophthalmos" if the person is unable to close their eyes at night.

There are several factors involved, and unless it's due to physical obstruction, lid archetecture (such as short lid length (due to surgery etc)), or facial nerve (CN VII) problems, it's not well understood.  

I have seen numerous people with varying degrees of this over the years.  For most of those people, it's an intermittent thing.

Tears are essential for eye tissue health, including cleaning and avoiding infection. People complain of dry or irritated eyes mostly.  But in more extensive cases, keratitis and ulcers can occur, which are bad.  If it's frequent, tell the person to make sure they tell their eye doctor (or if they don't have one, get it checked out sometime) so that the health of their eye tissue can be evaluated.

Another possibility is Grave's disease - in that condition, the entire eyeball protrudes and sometimes the eyelids aren't long enough to cover them adequately.  But what you're describing is probably not Grave's disease.

Wikipedia

American Academy of Ophthalmology