D Stanley is correct that "Short sellers do not destroy value any more than stock buyers create it."
But just like stock buyers can cause a company to succeed, short sellers sometimes cause companies to fail.
But short sellers can prevent the company from selling stock to stock buyers. By lowering the market capitalization of a company, they can reduce a potential lender's valuation of the company. This can prevent loans and preferred stock issuances. It also harms the morale of employees who are emotionally attached to the value of their shares and/or stock options.
If the company's long-term prospects are dependent on short-term actions (such as issuances of securities, or short-term employee morale), then the actions of short sellers can severely harm the long-term value of the company. Of course, any company whose long-term prospects are that dependent on its short-term actions is very risky.
Also, large short-sellers tend to research companies to find out reasons other investors or speculators might want to avoid owning the companies' securities. Furthermore, they tend to aggressively promote any findings that tend to lower the stock price.
Even in bubbles, stock buyers tend to reduce their purchases of a stock if they perceive to the stock to be too pricy. Whereas short sellers (especially ones who doubt the viability of a company) sell increasing amounts of a stock as it goes down. Sometimes they are forced by "short squeezes" to buy back large amounts of stock all at once. So short sellers can increase the volatility of a stock's price. This can increase the public's perception of a stock's riskiness, and thus reduce demand for the stock in the short-term and intermediate-term.