Unborrowable stock is the stock that no one is willing to lend out to short sellers. When shares in a company become unborrowable, the traditional means of short selling them is impossible.
Short selling a stock involves finding someone in the market that is willing to lend you the stock in the first place, and then buy it back when you close your position. Usually, finding short selling opportunities is the job of your broker, who will then pass the owner's borrowing costs on to you.
However, short selling can depress a share’s price on the market, and even bring about a bear market. For this reason, your broker may find it impossible to find a lender for a particular stock. In this instance, the stock has become unborrowable.