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Simba loses all hope after the death of his parents and the destruction of the Pride Lands in Series Four. He gets over it, though.
Similarly, he loses hope again in The End when the Writer kills all of his friends, including the love of his life, Nala.
Haiba for a brief while after he murders Tama.
In Fallout: Equestria The Massacre at Littlehorn, which involved the slaughter of an entire school of foals, signaled the end of any peaceful solutions to the Great War and sent Celestia over the DEH, stepping down as ruler and letting Luna take over
And after the war, Raiders are ponies who have been driven over the DEH by the blasted, inhospitable Wastes, losing all hope in everything and simply becoming agents of the brutality of the Wastelands, killing, torturing, raping, any pony they get their hooves on.
In Evangelion 303 Asuka goes through this. After Unit-04’s crash and Jessika’s death Asuka was wrecked with survivor guilt. Then, during the NF-14 test she learnt that she could not yet reuniting with Jessika. She did not get the acceptance that she longed for, and she nearly died. Her mood got worst and she attempted to commit suicide. When it did not work either, she ran away.
In The Death Of Princess Luna, Princess Celestia and Luna suffer this; the former suffering this having seen Luna's fake body in the Everfree Forest, and Luna thinking that nopony would save her from her captors planning to execute her. This is all averted when Twilight Sparkle and her friends find and rescue Luna and present her to Celestia, creating a heartwarming and tearful reunion.
In the Oneiroi Series, Redcloak rockets past it when his insane daughter rapes and kills him.
In the pro wrestling story, A Ring Of Their Own, this is the reason given for Molly Holly's retirement from WWE in 2005 (the story takes place in the kayfabe world) after getting her head shaved at WrestleMania 20 plus the losing streak and humiliation conga she went through afterwards. Only after a substantial amount of arm-twisting from her best friend, Ivory, does she agree to come out of retirement and join the new all-women wrestling company, the FWF.
In The Second Try, Shinji and Asuka are forced to this line a second time; the latter when going against Arael again, the former when he thinks Asuka is dead. Thankfully, this gets averted both times.
Vampire mate bonds and werewolf imprinting are said to be strong enough to cause this in Luminosity. The actual trope is commonly avoided, as the vampire either commits suicide offscreen or becomes The Unfettered, but when Edward thinks that he's lost Bella, all he does is ask to die.
The Villain Protagonist of the Mass Effect fanfic The Council Era endured this when he witnessed his wife's death on a news network. As part of his grief, he destroyed his entire clutch, except one, who soon after hatched. When the same soldiers who killed his wife, and were searching for him (he'd gone AWOL) surrounded his home, Tyrin threatened to kill his one hatched child and then himself. There's also a potential Alternate Character Interpretation that his criminal actions in the story are because he's caught in a state of perpetual despair following his wife's death, and is taking it out on the world.
In Revenge Road, Hikaru returns to Japan for an audition as a last effort to get Kyosuke to notice her, and then seemingly meets Kyosuke, who appears to have grown distant from Madoka, there. She fails the audition and learns that the Kyosuke she was with was a fake, then snaps and kills Kyosukeand Madoka.
Par for the course in A History Of Magic, considering it's a Puella Magi Madoka Magica fanfic, and if all the examples were listed we'd be here all day, so let's look at the one unique one that happened in the post-Madoka world. Homura kills Mitsuko in cold blood after she murdered Madoka's younger brother. Homura could not forgive herself for killing a fellow Magi, and believed herself beyond redemption. Had this been a pre-Madoka world, Homura would have become a witch. For most magi in the post-Madoka world, they'd just disappear. Homura becomes an Angel, a witch who retains her memories of her past life.
In another PMMM fic, To the Stars, in the Post-Madoka future during the Battle of Epsilon Eridani the magical girls and the normal human soldiers defending the colony world were brutally savaged by the aliens, and were about to cross the DEH, but avoided doing so when Homura Akemi, ironically, crossed her own: As her Soul Gem was practically pure-black from magic exhaustion, she pretty much resigned herself to die, something she was actually looking to since it means reuniting with Madoka. Except Madoka didn't want Homura to die, and so the latter was denied her wish, which pushed her over the edge, turned her normally angelic wings into dark-twisted wings as seen at the end of PMMM, and practically wins the battle by herself, and goes into self-exile afterwards.
In A Growing Affection, Minato's death pushes Gouki from avoiding the ninja world and helping the civilians who live nearby, to deciding to take over the world and enslave all ninjas to his will, so he can force them to put the rest of the world first.
In Chapter 8of Gensokyo 20XX, Yukari's reached this when her search for Ran, Chen, and Flandre left her empty handed, leaving her heartbroken and so upset with herself that not only did she feel she was unable to return to Reimu (to whom she had left behind to make sure she won't be captured) her frozen tears enclosed her in a cocoon of ice and she remained in that state for a couple of chapters, stating she was entombed in her cocoon of ice for a long time.
Be noted in said chapter, she also figured Reimu probably died during the time she was searching for Ran, Chen, and Flandre, meaning she felt she had nothing to go back to.
Aang and Co. seem to be nearing this after Zuko and Azula attack the Western Air Temple in TheMasksWeWear.
What makes his reply even sadder is that it sounds like a callback to his declaration when he meets the task force earlier on in canon that Justice Will Prevail and that he would "win the war" in spite of being childish and a sore loser. But this time, he's essentially admitting that the opposite happened BECAUSE he was being childish, just around the time the task force take Erin home and leave him for good.
In the MLP fanfic What Have You Done. Twilight does this after her friends abandon her at the Canterlot Wedding rehearsal but Chrysalis unlike in canon, just leaves Twilight instead of sending her to the caves, seeing as how Twilight was already in the depths of despair. Twilight leaves the wedding dejected frees Discord, and the Mane 6 and Twilight's mother find her Element of Magic pitch black.
I'm tired of it all, tired of whatever it is that's happened to Equestria. I've seen too much happen to Equestria to call it the same land I grew up in, and it's hollowed me out like an old Nightmare Night pumpkin.
I want my sister back and all I have is a monster with her face, a damn caricature that looks for all the world like her but has none of her soul inside. I want to tell her how I feel but I cower away like a foal away from her eyes. Eyes that no longer have that stubborn but warm love and care; just hatred and wrath for anything that goes against Queen Celestia and the so-called 'greater family and herd'.
In the The Lost Element, James is driven over the line after experiencing Discord's corruption of all his friends, while not knowing that they could be restored. While at first he is merely confused by the behavior of his friends, he then starts to worry. He finally loses it when Fluttershy makes an ultimatum where she will leave him for not being tough enough if he doesn't punch himself in the face with his strength boosting gauntlets on, and then make a cut in his neck using his sword. This causes him to not just break down, but to all but go insane, tricking Discord into a dual to the death where he dismembers Discord, eats his wings, rips the Elements of Harmony out of his chest, and generally kicks the utter humanity out of him until he is dead. Due to earlier events, all his friends see it and James finally has his moment of sorrow. This is made even worse by the fact that the author put the story on hiatus right after this chapter was completed, stating that he would continue the fanfiction once he was finished an alternate ending fic where James succumbs to his wounds after the battle. Given the fact that Humanity writes huge chapters, the main storyline won't be getting an update for a while.
In The End of Ends, Beast Boy crosses it sometime after running away, which prompts the Dark Prognosticus to come and lend him his power...
In Alabaster Orchestra, Ichigo is driven to this by the truth of his mother's death, the destruction of his Shinigami powers, and mental torture from Gremmy.
In Out Of The Dead Land, seeing Steve be killed causes Bucky to become so hollow with despair that he agrees to let HYDRA take him into custody again to mind-wipe the pain away and even fights off Natasha and Sam when they try to prevent him from doing it. It turns out that Bucky has more heroic spirit than Zola was counting on, however, and he summons the resolve to take down Zola and his robot army for once and for all even before he learns that Steve isn't actually dead.