What happens to the soul when one is put under anesthesia?

If you believe in the existence of a soul, separate from the body, do you believe that anything special happens to the soul when you’re put under anesthesia?
If you think about it, going under anesthseia is the closest thing most of us do to dying. It’s different from sleeping – you don’t dream, you don’t sense the passage of time. It’s kind of like simply disappearing for a few hours.