What if there was a large scale fraud on the exchange, and shares that were supposed to be owned by a person or fund were "owned" by several different people at

What if there was a large scale fraud on the exchange, and shares that were supposed to be owned by a person or fund were "owned" by several different people at once. Or can someone provide a reason that's impossible? Bearing in mind I've personally seen screwups with processing thousands of credit card transactions with a software update.