In Keychain of Creation, an Exalted webcomic, this is canonically how Abyssal Exalted get created, as shown in Renegade Deathknight Secret's backstory flashback. Her entire village is killed by a demonic plague, she's deathly ill, and just as she's given up all hope of living, the Neverborn show up and offers her Exaltation in exchange for servitude.
Chapter 63 is getting sadder and Lucy looks about at the horizon here.She was okay, then Mike ignored her existence. Now...
In Homestuck, Eridan crosses both this and the Moral Event Horizon in the same scene. He gives up any hope of beating Jack and defects to his side, killing off his unrequited love interest AND his species' only hope for revival in the process. This makes his Sgrub title, Prince of Hope, rather prophetic- it was later explained that "Prince" roughly translates to "Destroyer."
Later, Roxy crosses it too after a disastrous turn of events leaves nearly all of her friends dead and Rose, the alternate version of her mother who she had barely met, died in her arms. She later confesses to John that she thinks it would be better if they gave up so that they could be with their friends in the afterlife.
Trudy crosses this in General Protection Fault after seeing Nick, (whom she had loved) propose to Ki, which Ki accepts. She had been starting to regret her actions, but this pushes her even further, and she attempts suicide in the next arc in which she appears.
Very nearly everyone with a speaking part in Gone with the Blastwave, though it doesn't manifest in quite the usual way. Rather than some grand gesture like falling into an Angst Coma or being Driven to Suicidenote apart from that one guy from the Blue army who Ate His Gun, they've all just become desensitized to the constant bloodshed and are operating on some sort of Heroic Safe Mode.
Anna Enfield's from Sire lead a fairly troubled life which took a sharp turn when the sister that she shared a body with used it to murder their beloved uncle. Having seen herself kill someone she loved and knowing that her Hyde half could not do that unless she desired it, Anna turns a knife on herself and tries to commit suicide.
In Stand Still, Stay Silent the Battle of Kastrup was this for the Danish army. About ten years before the start of the story, they tried to retake part of the Forbidden Zone that used to be mainland Denmark only to have the entire force wiped out in a single night by one of the many threats roaming in the area. After this, they don't even send scouts there anymore.