Death is so frequently the lose condition in games that I think you could argue it's a little lazy. Don't get me wrong, I don't mind when a game threatens my game avatar with death. In fact I enjoy it as a threat. Morbid though it may be, I enjoy imaginary over-the-top violence and pretend gore in my entertainment. I suspect it's the adolescent thrill of something that makes other people squeal in discomfort that makes me enjoy them in entertainment, and so I play lots of games built around combat.
In fiction, heroes like Batman and Dr. Who and MacGyver never use guns, and narratively that invariably results in far more creative outcomes than a bullet ever could. Death is an easy and convenient fail state for a game, because we humans all understand that it's absolute, with no chance for reprieve. When you design a game or a game scenario where the lose condition isn't death, you have to think of other ways to inspire dread in players without threatening their avatars in the game with that same old boring penalty. Here are 5 examples of games that have been designed around death.
In many games inspired by Lovecraft or even Sherlock Holmes, you work to find clues that solve a mystery. The clues are often not actual clues, but tokens that represent the acquisition of evidence and comprehension. That means the players don't have to piece together a mystery, all they have to do is collect tokens. Once they have the right number of tokens, the player characters are said to have solved the mystery.
Admittedly, the implied consequence of any Lovecraftian game is usually the end of all reality, as in Pandemic: Reign of Cthulhu. After you awaken all the Elder Gods, Cthulhu awakens and devours the universe. That does involve death, but ending reality is a pretty abstract concept, and it's not something you can usually overcome with a fistfight. Players are rarely encouraged to literally fight against the end of the world in a Lovecraft game, and instead spend their efforts avoiding combat so they can gather important clues.
Classically, in a Lovecraft game, the greatest threat is loss of sanity. The idea is that the human mind can't withstand too much knowledge of the evil lurking just outside of our reality, and so prolonged exposure to that existential truth breaks a human's fragile eggshell mind.
It's pretty heavy stuff, and I admit it might not be the gentlest alternative to death as a fail state. However, it's worth considering because of how it changes game play. Instead of looking for somebody to punch or shoot, players spend the game searching for information. They ask questions, they explore, they go into the spooky places they normally wouldn't, because they're desperate for the truth.
The game Mansions of Madness does this both very well and very poorly. Most adventures for Mansions of Madness starts with exploration and investigation, but eventually, inevitably, disgruntled locals and dangerous cultists come round and force combat. I love the exploration and investigation component, but the combat feels out of place. The player characters aren't generally built for combat, and the combat system itself is just the same dice roll as any other skill check. It's not exciting and a little demoralising, especially when players are having all the fun they could ever want from the exploration and investigation part of the game. It's like having an awkwardly bad Game Master who doesn't know how to read the room before progressing to the next proscribed event, which makes sense because the "game master" for Mansions of Madness is an app.
Whatever the reason, it reveals much about the effectiveness of the natural fail state of a mystery. You may well finish the adventure and not solve the puzzle. That, as it turns out, can be just as threatening as death, and it can be a lot more fun when done well.
Forbidden Island is a cooperative game that really really has no death (not even the end of all reality). The titular island, represented by a tiled game board, "sinks" into the ocean as you play, taking all of the island's hidden artefacts with it, but the player avatars aren't directly threatened. In fact, even when your avatar falls into the ocean when a tile beneath you sinks, you're shunted to the nearest dry tile. There's finality to the fail state, but never death.
You fail by losing access to the win condition.
The heist genre generally doesn't threaten death. As with most heist movies, the threat is getting caught by the museum guards or the police. How the heist itself is expressed depends on the game. Some games have a planning phase, the way heist movies do. Other games, like Burgle Bros., place you straight into the action, letting you draw cards to gain special abilities that represent the elaborate plans you [pretend] made in advance. It's very often as much a winning formula in game form as it is in movie form, and the stakes are simply that you may not do as well as you could have.
The threat isn't death, it's that you're going to get captured.
In games like City of the Great Machine and Scotland Yard, you chase a culprit on the run. Broadly known as "hidden movement" games, there are several games structured around one player controling an objective that gets secretly moved around the board while all other players attempt to catch it based on clues left after each secret move. The threat of losing track of the important thing is a great lose condition, whether the thing is moving secretly around the board or whether it's just the stated threat of failure.
Chases can get boring if they're not done well, but even just the threat of losing possession of a thing you had is a good lose condition. The Dungeoneer deck Realm of the Ice Witch has a few "escort" missions in which your avatar gains some object that needs to be taken back to some special location on the map. If you take damage while you have the item, you lose the item, or else you lose some part of an item and only get half credit for delivery, or whatever. It works well, and the complication that penalizes you doesn't have to be combat.
Wargames are classically about death. And yet most wargames aren't actually just about clobbering each other until you run out of people to clobber. Instead, wargames often set objectives, such as controlling a specific site on the map, or capturing a flag, or finding an important object. The killing part is a significant concurrent complication for each opposing side, but the concept of controlling an objective over the span of several rounds in order to accumulate victory points is a useful one.
You can structure a game around a player's ability to maintain a specific game state.
Death in gaming is one of those themes that can influence design. When you approach a game with the assumption that losing is permanent player removal, then you design the game for removal. When you look at alternate fail states, though, you often make new mechanics available to yourself.