questions regarding merge of a publicly traded company to another publicly traded company?

When a company, say A, buys another company, say B, for cash i.e. X amount per share and the board of directors of B approves it, does the shareholders of the B company have the legal obligation to sell its shares to the A compnay. If not, what are the options? If a shareholder doesn't tender its shares by the due date what happens to the value of that share?