Is it normal to sleep with one eye open?
Sleeping with one eye partly open can happen, though it’s less common than sleeping with both eyes closed. If it happens regularly or leaves your eye dry, irritated, or painful, it’s worth getting checked.
If you mean literally, some people’s eyelids don’t close all the way during sleep, so one eye may look partly open. It can be harmless, but it’s less common than sleeping with both eyes closed—and it’s not the same as your brain consciously staying alert.
If it happens often, or you wake up with dryness, redness, irritation, or pain, ask a healthcare professional about it; an eye that stays exposed can get irritated. If you mean “sleeping with one eye open” as in being on guard, that’s a figure of speech, usually for feeling watchful or uneasy.