Is there person without consciousness? If we consider person(Arthma) as a consciousness. When undergoing an operation, we are temporarily unconscious. Then what happens to that person while unconscious?  

Some related discussion are here:

I want to understand the technicality of rebirth and what happens to conditioned self.
If there is no soul, how can there be rebirth?.
Is rebirth a delusional belief?.
What are examples of identity-view?


If we say these things are temporary illusions then how it is continued?  
What are the similes use to explain this phenomena in any tradition?
Nothing happens to that person when consciousness ceases - there was never a person to begin with, only arising and ceasing of experience.

I realized after the fact that I can't sufficiently cite sources while on my phone - apologies for such an incomplete answer, I'll try and expand later :)