Lampshaded in an Old World of Darkness sourcebook where they discourage relying too heavily on this trope: "If your character is taunted by classmates everyday, and every night is beaten and/or raped by his alcoholic father while his mother sits around dosed to her eyeballs on tranquilizers, you're laying it on kind of thick." In the New World of Darkness, such a person would have a better life than most of the games's player characters, though there's nothing that says you can't have a happy backstory. Prometheans, on the other hand, would look at that mortal and ask if they can trade lives.
In stark contrast to Geist stands Changeling: The Lost, where your character at the very LEAST was kidnapped, replaced, beaten, violated, and tortured for no reason! Even if their back-story makes them more of a Break the Haughty, you still want to give them a hug. As the page puts it, "Touched by Vorlons: Molested by Vorlons is more like it."
In Werewolf: The Apocalypse, the Bastet had a Gift called "Kitten's Cry" that basically made them look like an adorably cute Woobie on command.
In Hunter The Reckoning, those of the Innocence creed could gain a similar power to the "Kitten's Cry" called "Staredown." It only worked in combat, but when an Innocent refuses to fight the monster that's about to rip into him, something in the latent humanity of the monster stops them from attacking because it has suddenly realized that harming this wonderful, innocent person would just be a travesty against all things right and beautiful, blah, blah, blah. It is justified, in a manner of speaking, because one has to embody the Innocence creed pretty closely to attain this power, whereas there is no such thing as a Bastet that is not dangerous.
Lilith in Exalted. Let's put it this way: 3000 years in the heart of pure insane chaos did less psychological harm than her marriage to the monstrous Desus did.
The weakest and kindest of the Primordials, Autochthon The Great Maker qualifies for some; he spent literally billions of unknown aeons being bullied and mocked by his siblings for being weaker and the runt of their kind; when his revenge schemes with the Exalted not only mutilated but outright killed a few of them (transforming them into theNeverborn) he was horrified at what he'd done. Since then, he's been consumed more and more by his disturbingly cancer-like sickness, and in the current setting, it's highly likely that he'll die himself.
One of the D&D-based Choose Your Own Adventure books, Return to Brookmere, has a scene where the elf hero finds a young gnoll crying its eyes out, having been abandoned by its tribe for admiring pretty things like jewelery and disliking other gnolls' brutality and mayhem. Perhaps the earliest published example of Woobieism in an Always Chaotic Evil D&D race.
The race of shadow elves, from the Mystara setting, are a deliberate subversion of D&D's own Subterranean Elf = Chaotic Evil Drow trope. The product that introduces them gives their culture a history steeped in Woobieism — driven underground by nuclear disasters (yes, plural nuclear disasters), harried by horrific monsters at every turn, cold-heartedly exploited by their own Immortal patron, and branded as evil freaks by surface elves — the better to subvert gamers' expectations about deep elves.
Corax, the Raven Guard Primarch. His legion was so horribly slaughtered after the Isstvan V Drop Site Massacre that they were thrown out of the fighting for most of the Horus Heresy, and Corax had to rebuild. He resorted to desperate measures, but in the end he was left with the majority of the recruits mutated into horrific monstrosities. After personally and reluctantly Mercy Killing the marines his orders had created, he was overcome with grief and remorse, and locked himself in a room and didn't leave for over a year, praying for both their souls and his. When he emerged, he took his ship and flew it straight into the Eye of Terror, his last recorded words being "never more".
The Eldar Healing Goddess Isha, practically the only kind and loving Warp-entity there is. So of course, loads of bad shit happens to her. She created the Eldar, only for Kaela Mensha Khaine to start wiping them out after he saw a prophecy that they'd one day kill him. When she went to Asuryan to get him to stop, Asuryan's response was basically "cry me a river", and that's exactly what she started to do. Eventually Asuryan relented and ordered the other Gods to stop interacting with the Eldar. Isha cheered up a bit until she found out that he meant all interaction. So Isha began meeting her little creations in secret, but Khaine found out about it and had her imprisoned. When The Fall happened, Slaanesh killed her husband Kurnous and tried to eat her, but Nurgle saw her, fell madly in love with her and saved her from Slaanesh. That's good, right? Well, no. Nurgle is the Chaos God of Pestilence, so chances are he is utterly disgusting to look at, and if that's not all, he keeps her locked in a cage next to his big disease-stirring cauldron and uses her a guinea pig for his creations. Fortunately, she's the Goddess of Healing so she can recover from them, but that therein is the problem. So... Yeah, she's stuck there, being fed horrible diseases without any hope of reprieve, and her only solace is that she can use moments of Nurgle's distraction to whisper the cures for his diseases to the mortal races she loves so much. Poor, poor Isha.
Szarekh, the Silent King of the Necrons is a major one. Seeing the Necrontyr empire collapse during the war with the Old Ones, he struck a deal withthe C'tan in order to let the Necrontyr win. He was tricked by the C'Tan, who turned his people into the soulless automatons known as the Necrons. After the war with the Old Ones ended, he turned on the C'Tan, and blasted them into shards, but the efforts to stop the C'Tan left the Necrons exhausted, unable to keep their empire running. He then went into a self-imposed exile in intergalactic space, as penance for his actions. Guy seriously needs a hug.
Characters with Aww!, Offering you Comfort, or Thumbs-Up Emotion XP in Chuubo's Marvelous Wish-Granting Engine tend to fall under either this or one of the subtypes. The pregen character who best defines this rather than anysubtropes would be Seizhi/Suzy, the Best Friend, who is very stressed out over not being real and kind of needs a hug.