The article is about Utah state legislation to protect Utah companies but the description of naked shorts and phantom shares applies to any trading stock:
Stock transactions are supposed to clear in three days. It is the responsibility of the broker-dealer handling a transaction to locate the stock, or at least have reasonable belief that he will be able to locate the stock, and make sure it gets delivered to the buyer. If that delivery doesn't happen, the trade is deemed "failed to deliver."
Most times, failures are cleared up in a matter of hours or days and are related merely to administrative snafus.
But people like Byrne contend that aggressive short-sellers also can manipulate the system (with broker-dealers looking the other way) and trade, despite getting "fails-to-deliver." That's what's called naked short-selling. In effect, it creates phantom shares in a company and drives down the price of its stock.