A bear hug is an informal offer to acquire a company at a premium to the market price of its shares, made public without the consent of its board.
Bear hugs rely on the fact that the shareholders of the company will put pressure on the board to accept the proposed terms or start negotiations with the offeror.
If the target company refuses to accept the bear hug, it risks being prosecuted or challenged in board elections.
Without a tender offer for outstanding shares, a bear hug is no guarantee that a bidder will buy the company at the stated price.