If you do not avail of a tender offer, this means that you wish to keep your shares. There are some tender offers in which the offer price is lower than the market price of a stock and it is a better option to not avail of the tender offer.
Just note that if the stock announced an intent to delist then availing of the tender offer or selling the shares in the market would be a better option. To delist would mean that the stock company plans to be taken out of the stock exchange at a specific date. Should you have shares after the delisting date then you would need to convert your scripless/electronic shares into stock certificates which will entail submission of forms, payment of fees and sometimes personal appearance at the company's stock transfer office. Stock certificates of delisted companies will be kept by the shareholders, will no longer reflect in your COL portfolio and would be more difficult to sell. Selling stock certificates will be done through the stock transfer office rather than the stock exchange.