It depends on whether the old chain is even viable. Unlike bitcoincash, there is no EDA to move the difficulty down quickly, so it might just get stuck where people can't send anything. If that is the case, it will die.
Interestingly, Bitcoin Cash is aiming to hard fork within the next couple weeks to remove the EDA and get back to a predictable 10-minute block time. If you think about their scaling vision (massive block size and.....not sure what else), the EDA didn't make sense. It seemed like a gimmick that exploited peoples' frustration with network congestion just to let Bitmain pocket more block rewards.
Whether or not the legacy chain is viable, it's become clear that it will still have a strong community even if the 2x chain "wins." If it's truly stuck, I'm quite sure that the legacy chain will be forked to change POW or lower difficulty and there will be demand for these coins. It will be ugly, and we might see some Core developers move on to other projects, but in the end, the corporate takeover attempt will fail.