Naked short selling
Naked short selling is the (illegal) practice of short selling a stock without first borrowing the shares.
A short sale involves borrowing shares from somebody else and then selling them, with the requirement to buy them back at some point in the future. But, there is a delay between the actual selling and the delivery of those borrowed shares which were sold. A bit confusing, yes, but real. The shares are sold before they are actually received by the one borrowing them. The delay, by law, cannot be longer than three days. Until those borrowed shares are delivered to the one who sold them short, the position is "naked."
However, it is possible that the borrowed shares are never delivered. In this case, the naked position remains and now there are shares that have been sold which never existed in the first place. This condition is illegal, but enforcement of the delivery time is not strict. Brokers, who earn commissions from the short sales, do not have a major incentive to always deliver the shares to the short seller. This can lead, in extreme conditions, to more shares being sold short than actually exist in the float.
An investor may come across the term "Reg SHO list". These are, essentially, stocks whose shares are shares have been sold short in a naked condition. According to the New York Stock Exchange, "A Threshold Security is defined by Rule 203(c)(6) of the SEC's Regulation SHO as any equity security of an issuer that is registered under Section 12, or that is required to file reports pursuant to Section 15(d) of the Exchange Act where for five consecutive settlement days: (1) there are aggregate fails to deliver at a registered clearing agency of 10,000 shares or more per security; (2) the level of fails is equal to at least one-half of one percent of the issuer's total shares outstanding; and (3) the security is included on a list published by a self regulatory organization." 
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