The person may look normal and healthy on the outside, and all their internal organs and whatnot seems to be functioning okay, but their soul is gone.  I think Ray Bradbury may have written a short story dealing with this very theme, and there's also a rare mental condition where the person thinks they’ve died and are still somehow walking around.

Also I saw this cartoon on Facebook a while back depicting this man getting up in the morning, and he's nothing left but a oozing black shadow and he goes to his closet and slips on this human skin costume. In the last panel, he's walking around in his fake human skin with fake smile greeting people in the park.