HOW IT WORKS
A corporate raider engaged in greenmail requires a takeover vehicle to launch a hostile takeover. The takeover vehicle is usually another corporation controlled by the raider, although in recent years ESOPs have been used (e.g., Tribune Corp., 2007). The vehicle buys up a lot of shares of the target company's stock on the market, then announces it wants to acquire a controlling interest.
Management opposes the takeover bid. It can (a) challenge the legality of the takeover, (b) adopt a charter that makes it hard for the takeover vehicle to run the company it's proposing to buy (a poison pill), (c) seek another buyer that is more favorable (a white knight), or (d) borrow a ton of money and buy so many shares that the stock price goes up.
The raider makes a tender offer for the shares he doesn't own. If the target picks (c) or (d), then the raider will probably make a huge amount of money when he suddenly dumps all his shares on the market. His tender offer probably started a bidding war with management, driving share prices to something very high.
WHAT CAN GO WRONG
The management can use (a) or (b) successfully, or it can use (e), viz., launch a hostile takeover bid of the target vehicle. The raider can lose of lot of money if a lot of shareholders have accepted his tender offer.