"In that situation, what happens to the non exhistant shares that you bought? You paid real money for them. Are you reimbursed or are you S.O.L? Or would you have to try and recoup your money with a lawsuit?"
If the money was taken out of your account and the shares are listed in your portfolio then they are 100% yours. The seller provided the shares to your broker likely "in trust" which means that they promise to provide the share paper if it is ever requested by you but quite frankly this never happens. The reason is that most brokers charge $50 to ship you the actual real shares.
Most of these transactions are electronic and like real money, what is trading out there in electronic means is quite a bit larger than the money that actually exists. It is only when a company is sold or the tally at an AGM vote exceeds the total number of issued shares that the actual number is ever looked at.
A long shot but one that would make for a very interesting result if it were to happen.
M1.