A tender offer is a voluntary corporate-action: you must instruct your broker to tender, and the broker's deadline precedes the official one. Offers are usually conditioned on a minimum acceptance level, and if more shares are tendered than sought the offer is prorated.
Once an acquirer crosses a high threshold, often 90%, remaining holders can be squeezed out in a short-form merger at the same price, so holding out rarely gains anything.
Example: a company offers to buy 20M of its 100M shares at $46 while the stock trades at $40. Holders tender 40M shares. With a 50% proration, tendering 1,000 shares sells 500 at $46 and leaves 500 in the market.
Related: dutch-auction-tender, share-buyback, acquisition, merger-arbitrage