When Matt Coleville proposed the "Chain of Acheron" campaign to his players he told them that the game would take place after a major defeat for the Chain, and that they would be playing the story of building the Chain back up to face their enemy. He then told his players they would be playing that first defeat. The players showed up for the first session knowing that they were going into a battle that they were going to lose, and lose hard.
It's an interesting idea. One I want to try. Fortunately, a game I am in just started the same way. We all chose to do a Star Wars "Rebel Special Forces" game, and to start things off the GM had us all be part of a mission that went horribly wrong. As the survivors of "Operation: Good News" we would be brought into Rebel Special Forces for the game. Of course, the first session was going to be Operation: Good News itself.
As a player this excited me. It was a lot of fun going into the game knowing that this mission was going to go bad. This mission was going to be painful. It could kill PCs - in which case they'd have new PCs going forward - and it would likely kill any friendly NPCs involved. The question wasn't "will the PCs do this thing" but rather "How will this thing go bad?" and "What will the PCs do when it does?"
In practice I found this liberating. I know RPGs aren't "games you have to win" but part of my brain always wants that. It wants the PCs to succeed. It doesn't want the mission failure screen. Knowing going in this mission was going to be a fail meant that part of my brain was turned off. Instead I was just in "enjoy the ride" moment. At least, it was for the most part. In full truth my brain was working on a different question: how do I help make this dramatic?
Other common problems you can run into in an encounter turned bad didn't happen. There was no attempt to "hold the line" as PCs when opposition came onto the board. There was no thought to standard PC heroism. The PCs made a fighting withdrawl, working to keep people as alive as possible.
For me - at least - it was a lot of fun. Plus, there is the added benefit that all our characters now have this common touch point. We all survived Operation Good News. We all experienced it. Whatever happens next in the game, that can be used to form a real group bond.
Coleville has the same going on - in a bit of a longer format. You can check that out at the MCDM youtube page. But this intro is one I definitely like, and maybe someday soon I'll get to use it.