What will happen to my green card?

The general answer I can give you here is that if the new Co. acquiring the existing one (referred-to as the "successor in interest") will purchase not only the assets of the co., but also all its liabilities (now this is important, for it includes all the "green card petition obligations" of the co.), then your 'green card process" will proceed as previously planned, but with the necessary amendments filed by the successor in interest co., through its immigration attorneys.

The purchasing company can continue the green card process; however, at the same time, the company could elect not to continue the process.

The acquisition document holds the answer. If the successor in interest will continue to support the immigration obligations, your green card process will continue.