Well, actually it is usually the other way around. When a company wants to take over another company, they usually announce a price with 20-30% bonus. So, that results in surging the price of the stock of the company that is being made an offer with a hope that there will be a better offer. But that was not the case with the Bear Stearns, for it was offered an extremely low price, and hence freaked out the investors.
As for my example, you are right XYZ needs to have the majority, but there are rules that XYZ must compy as well. It must be willing to purchase all the remaining shares with the announced price up to the announced date. As for forgetting to sell, usually the stock goes out of market before the tender offer is due. So your last chance would be to submit to the company for the announced price. If you pass the deadline, your shares are worthless.