All outstanding shares of stock are eligible for dividends, and that includes shares that have been sold short. What complicates things is that such shares have been borrowed from one party and sold to another, so each share essentially has two "owners" expecting a dividend.
Short Selling Walkthrough
Short selling allows a trader to profit from falling stock prices. The short seller borrows a number of shares, usually from a broker, and sells them at the current market price. Later, when the market price falls, the short seller purchases the same number of shares and returns them to the broker. The difference between the sale price of the borrowed shares and the purchase price of the replacement shares is the short seller's profit. (Of course, if the price rises instead of falls, the short seller loses money.)
Say you're "short" 100 shares of XYZ Corp., meaning you've borrowed 100 shares from your broker, have sold those shares and are waiting for the price to fall so you can "cover" your position (that is, buy replacement shares). Now say XYZ Corp. pays a dividend of $1 a share. The dividend for the shares you borrowed will be paid to the people you sold them to. As far as XYZ is concerned, those people are the rightful owners of the shares.
Back to Your Broker
As far as your broker is concerned, however, he still "owns" 100 shares of XYZ Corp. He just happened to let you borrow them for a while. As a result, he expects to get $100 worth of dividends. He's not going to get that money from XYZ Corp., which paid the dividends to the current shareholders. So he's going to get it from you. Short sellers are responsible for paying the value of the "missing" dividend to whoever lent them the shares in the first place.
Factoring in the Cost
Short sellers need to factor in the cost of any dividends when calculating where they stand. If you've shorted 100 shares of a stock and the price has fallen $1 a share, you're ahead $100. But if the company has paid a $1-per-share dividend since you borrowed the shares, you're only breaking even. Companies don't typically pay dividends out of the blue; they announce them in advance. Short sellers can then take those future dividends into account when planning their strategy.