The shares will continue trade after an offer comes in (after an initial trading halt to announce). There is usually plenty of time between the bidder making the offer and closing the deal.
Some examples worth looking at are Afterpay (scrip deal that went to shareholder vote) and Tietto (full cash off-market takeover). Both took several months, and both companies shares traded at or about the bid price for the entire time between the initial offer and the final closing.
That this means for those with options: you will likely have sufficient time to convert before the final sale.
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