At least with European carriers (with flight to/from USA) each time I've been offered to take a later flight it has been at the check-in or bag drop, I've been

At least with European carriers (with flight to/from USA) each time I've been offered to take a later flight it has been at the check-in or bag drop, I've been informed that should I accept I'd get a boarding pass and should go to the gate where they would eventually tell me whether I'm flying or not. So, no surprises there, ever. They gather a group of passengers willing to trade their flights and pick flyers vs hotel goers among those.