As far as Iunderstand and i may be wrong but your soul is contained inside your body. When you are anaesthetised its as you say your put into a false coma but all your organs are functioning and your not dead so your soul should remain in your body.
Altho there are some who have said they have had out of body experiences , where their soul has apparently left the body. I dont know if this is true or not , I would like to think it is.
When someone does die i always open the window to let the soul out , all based on tradition , not fact of course.