In bad fanfiction (especially of the Jerk Sue or Sympathetic Sue kind), one EXTREMELY common plot device is to make the parents of one of the characters physically, emotionally, sexually and/or mentally abusive, to throw said character in the arms of his/her True Love.
Heck, even doujinshi use this cliché. In one of NEGAHYST Circle's The Prince of Tennis dj, both Masaharu Niou and his mother are routinely abused by Niou's alcoholic father (with said alcohol problems being nwhere found in canon since we barely know about niou's parents), and it's used as a flimsy plot device to make Niou wangst and throw him in his partner Hiroshi Yagyuu's arms.
Son Of Apophis, a Yu-Gi-Oh! fanfic, takes the abuse Marik experiences to a whole new level. His father actually attempts to mute him.
Pick any Naruto fan-fiction where Hiashi Hyuuga is a main or supporting character. In 90% of those works, he's shown as being verbally, psychologically, emotionally, and sometimes physically abusive toward Hinata; Team 8 is one example of all four types in action in the same story. (Ironically, the remaining 10% tend to portray him the way he was and currently is in canon—emotionally distant, but not such a bad guy once Character Development sets in.)
Nobody Dies, a Neon Genesis Evangelion fanfic, features Kyoko Zeppelin Sohryu, who in this continuity was not driven insane by the contact experiments. She emotionally abuses Asuka, turning her into a Shrinking Violet, rather than the Jerkass that Asuka was in the series. In an interesting semi-aversion, Kyoko realizes her mistakes when the other NERV personnel nearly murder her for it, and resolves to try to become a better person. She and Asuka are now on at least amicable terms.