Yes, some do. Rabbits developed the skill of sleeping with their eyes open as a defense mechanism. With that, they can appear awake, so predators will think twice before attacking them, and they can also notice danger even while they’re asleep. It’s is possible because rabbits actually have a third eyelid. It’s called the nictitating membrane, and it’s a translucent film that closes while the rabbit is sleeping to keep their eyes from drying.

It’s believed that humans used to have a third eyelid, too – the little pink thing in the corner of our eyes is called plica semilunaris and are remnants of a nictitating membrane. It’s vestigial, meaning it’s now functionless. Why we lost it in our evolution is unclear. Imagine if we didn’t, we could sleep in class, and the teacher wouldn’t even know, haha.