Mining may be a bit of problem with this idea, but right now I'm just trying to figure out major flaws. This is a really weird concept but here I go:

Imagine a crypto currency where everyone owns the maximum amount of coins (22 million in bitcoins case) and having more than 22 million should be impossible, and having wealth is simply having 22 million minus x. Why have this backward ass system? Think about how transactions would work in this system, for Alice to pay Bob, Alice has to accept coins from Bob. The direction the coins move is opposite of that of bitcoin. Thus instead of the person who is sending wealth being able to be an attacker, the receiver becomes the possible attacker, but why would he sabotage receiving wealth?

There are hurdles that I can clearly see, like mining and how to prevent anyone having more than 22 million, but is my idea sound?