Suppose you have a flight with two segments (booked together on a single ticket on the same airline). You find out before boarding the first segment that the first segment is delayed but the second segment is not expected to be delayed, so you will miss the connection to the second segment, which is the last flight of the day from the connecting airport to your destination.

But there are other non-delayed flights from your originating city on other airlines that you have time to get onto.

Will the airline you are booked on be willing to put you on one of those other airlines' flights to get you to your destination without too much delay, or will they insist on sending you on their own flight, ensuring that you will miss the connection and not get to your destination until the next day?