It means a blow-up person with no air in it. A blow-up person usually refers to a life-sized plastic "doll" that you blow up (like you blow up or inflate a balloon). So it could be thought of as a big balloon shaped like a person. Except a deflated one would have no air in it. Either it hasn't been inflated or it was inflated and then deflated, possibly because of a leak.

To follow on from Alan's explanation, if you use this to describe a real human being, you mean that person has no personality (ie. full of air... "a blow-up person"), and at that moment, what ever the "air" was (ego? money? attention?) is now gone.