They say that portrait photos should always have the eyes open because the eyes are the window to the soul. This is probably true 98% of the time. But like all rules there are times to break them. Photos can be very expressive with eyes shut.
I recently had a photoshoot with a friend and one of the first things I told her was to make sure she keeps her eyes open.
As you can see above, despite her eyes being closed, the photo is very expressive. It's actually one of my favorites from the shoot. There's something about it that creates a connection.
Is this something I would suggest all the time? No, but if a reflective or introspective mood is what you're after then give it a go.