Basic Trope: A character who bends plot, narration, and Willing Suspension of Disbelief so that other characters (as well as the reader, in theory) can pity her.
Straight: Alice lost her parents in a car accident at 15, was raped at 18, and became addicted to meth at 19. She and/or the narrator mention(s) this at every opportunity, and other characters freely shower her with all the pity and special treatment they can possibly spare.
Exaggerated: Alice was raped, beaten, and forced to watch 2 Girls 1 Cup by her father and her mother — who, afterwards, both died in a car accident without ever getting to apologize to her for this treatment— every single night until she was 16, after which her boyfriend took over. She wears a sandwich board explaining this in detail, and can freely rob banks because the police feel too sorry for her to arrest her.
Downplayed: Alice lost her parents in a car accident at 15. The story loves to remind us of this whenever it's relevant, but it doesn't really shove that knowledge into pieces of the story that aren't affected by Alice's orphan status.
Justified: The people around Alice were predisposed to be sympathetic, for whatever reason, and tend became blind to the fact that it's the same story. This leads to Alice, and by extension, the narration to keep going on about the issue, Alice trying to milk this, but still having enough sense to stop before her peers would start being negatively affected by this.
Alice had the happiest childhood ever, never having been grounded, raped, abused or even used drugs at all. She doesn't want any pity at all, and doesn't care about it.
Subverted: Alice moans endlessly to someone about how her parents died in a car accident... only to have her mother call her on her cell phone and inquire in a very loud voice as to whether she remembered to bring an extra pair of clean underpants (just in case).
Double Subverted: Alice then whines — even more loudly this time — about how overbearing her mother is and why can't she just leave her alone? The narration takes care to explain in detail why it is every woman's inalienable right to choose how many spare sets of undergarments she has and in what condition they are in and how Alice's mother is a horrible monster for daring to impose her ideologies on her daughter.
Parodied: Alice notices that her story about how she got raped in a back alley at midnight in the bad part of town is starting to lose its impact. She then adopts an adorable puppy and names it Mr. Muffins, after which she lets it off its leash at a busy intersection and crosses her fingers.
Zig-Zagged: Alice has been through hell and back thrice and whines endlessly about it... but the other characters mostly just get annoyed. The narration, while wholly supportive of the other character's right to be irritated by Alice's endless moaning, nonetheless brings it up at every opportunity and makes sure the reader knows just how much Alice should be pitied.
Alice has been through more than her share of tragedy, but it more-or-less makes sense and Alice has gotten/is trying to get past it. Neither Alice nor the narration parade her suffering around just to get sympathy.
Enforced: 1) "Bob from TVTropes The Internet-based Anime Cartoon Movie (based on the best-selling comic book!) has a traumatic back-story." 2) "I think Bob is an interesting character." 3) "Therefore, characters with traumatic back stories are interesting." 4) "By extension, the more trauma a character has, the more interesting they are." 5) "As such, my fanfic will have an OC named Alice who has suffered every tragedy conceivable by mortal minds." 6) "Also, since the tragedy is what makes Alice interesting, no less than 50% of each paragraph will go towards describing her pain in minute detail."
Invoked: Alice notes that telling people about that one time, behind the 7-11 is an easy way to get attention, and consciously decides to tell people about it every chance she gets; additionally, she begins to engage in risky behavior in the hope that she'll get "lucky".
Exploited: Jamie sneaks out of the house while Alice unintentionally distracts everyone with her tragic past.
Alice notes that everyone seems to want to hear about her traumatic backstory, which itself is mostly just a series of random tragedies that could happen to anyone but, inexplicably, decided that they should all happen to her; from this, she concludes that she is in a sue-fic and promptly clams up in order to preserve the reader's sanity.
Alice wants to tell them about her Dark and Troubled Past, but no one wants to hear it out of fear of invoking this trope.
Deconstructed: The other characters feel too sorry for Alice to show her anything other than love and comfort, even though they secretly resent her for the special treatment she gets for her whining. Alice, meanwhile, has come to associate complaining about her pain with receiving sympathy and attention that temporarily alleviates said pain, and as such has no motivation to deal with her grief maturely.
Reconstructed: Alice has a horrible (but not nonsensically-so) backstory and is deeply traumatized, but doesn't talk about it much. The story, told from several perspectives, is about the (at least semi-realistic) reactions of the people around her as they learn details about her past.