So many good thoughts in this thread.
I've played a few games where people were generally pretty okay with 'losing' in some sense (losing an arm, having serious injuries, occasionally a death), and also games where people really weren't. I've never played a game where EVERYONE was okay with the losing, or even where most people were okay with ALL SORTS of losing, so I think one thing to recognize is that there's a sliding scale here.
Not all losses are created equal. I'm one of those players who generally does NOT want my characters to die, unless I'm just done with that character. CG is hard for me and I tend toward slow burn on character arcs and hate when they get cut short. But I'm pretty okay with big injuries and setbacks.
The games where people were more okay with losses tended to have certain things in common.
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Culture. Most of them were started with groups of friends who lean heavy on the story side of things instead of the game side of things. Having a solid core of players who are willing to fuck up sets a tone that makes it easier for new players to also be willing to fuck up. This is a hard thing to accomplish if you don't just happen to have a fuck-up-okay core playerbase sitting around, but I do think that it's worth thinking about how one sets the culture and tone of a game on opening.
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Smallish. I think that in many ways, several of these games had a similar feel to the tabletop stuff @faraday is talking about. We're talking probably 25 or fewer players, 35 or fewer active characters, and a ton of GMing work. The sort that is not really scalable to bigger games.
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PvE, single faction. No PvP in sight, beyond personal disagreements. Everyone working toward the same goal. Factions WITH a goal to work toward. This means that the group could have a success even while an individual had a failure (Incidentally, the bigger pushback on these games tended to be when the group had a failure). The single goal also means that there was a group sort of trajectory toward winning, even if this specific event was a set back or a loss.
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Largely consent. Some had no system at all, one had FS3, where the results of combat were in the hands of the dice, but death and permanent maiming were consent-only and generally you assume that the dice are going to be /largely/ in your favor. Being able to choose when and where and to some extent, what, makes it easier, I think. This is how you get players going 'YES CUT OFF MY ARM PLEASE!'
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Failures and losses get attention, and sometimes badass compensation. None of these games had coded rewards for these things outside of attention - but man did you get LOTS and LOTS of attention. Kill off a character? Watch people RP about you for weeks! Cut off an arm? NEW METAL ARM + lots of meaningful RP around topics like identity and loss. I'm someone who, as mentioned, HATES killing characters, but I killed two of them in this way, because both times it felt like it MEANT something. It did not pass unnoticed into the night, it generated a lot of RP. Technically it was a loss, but for me it FELT like a win.
I'm painting a bit of a rosy picture here, and I'm sure there were losses on these games that did not feel meaningful to people and did not result in the attention they may have craved, and that there were people who hated having them and who preferred to win all the time (in fact, I know there were, because sometimes they complained), but I still think that overall, there was a trend toward feeling comfortable doing stuff that was fun story and not just winning.
I'll also note that I think generally it's easier to take a loss that isn't your character's fault than one that is. To have your arm blown off or to lose in combat because that's how the dice roll than to not save your friends because you made a bad decision. Those sorts of failures do show up, but not nearly as often as the others. It's way less fun to RP for months about your bad tactical decision that got all the NPC kids killed than about how sad it is that you have terrible scars on your face now.
