Beacon chain is live with over $5 billion in ETH deposited so far, and has been running flawlessly since its December 1 launch. There are minor tweaks coming this summer. A few months after that, if everything still looks good, they'll migrate the legacy chain to it and proof-of-work on Ethereum will end.
The migration is a decent amount of work but it's not the difficult research task that the beacon chain was. Someone did a proof-of-concept in about a day, though the exact plan has changed since then.
If no one wants to buy the old ETH, then it won't be profitable to mine, so no one will mine it. Without mining there is no security (as far as the old PoW chain is concerned.)
Kind of like how Ethereum Classic (ETC) is subject to 51% attacks every other week and requires multiple days' worth of confirmations after deposit to any exchange.
The migration is a decent amount of work but it's not the difficult research task that the beacon chain was. Someone did a proof-of-concept in about a day, though the exact plan has changed since then.