Tekken 6 Storyline
Xiaoyu was relieved to hear that Heihachi Mishima was still alive. She later learned that Jin Kazama, who had become the head of the Mishima Zaibatsu, was out to eliminate Heihachi. Xiaoyu intended to persuade Jin to stop, but she was unable to approach him due to the Mishima Zaibatsu's military buildup.
The King of Iron Fist Tournament 6 was announced just as the world fell into chaos in the wake of the Mishima Zaibatsu's war declaration.. Xiaoyu decided to enter the event for a chance to make Jin change his evil ways.
Source: tekken.namco.com
Tekken 5 Storyline
Ling Xiaoyu cried when she learnt of Heihachi's fate. In her sorrow, she wished she could go back in time and alter history. Having met a self-proclaimed genius who boasted he could invent a time machine if only he had the money, Ling Xiaoyu decided to enter the King of Iron Fist Tournament 5 to fund the invention. To go forward, she must first travel back...
Source: Tekken 5 Manual
Tekken 4 Storyline
Since the disappearance of Jin Kazama several years ago, Ling Xiaoyu had heard no news of him. Although still working on her fighting techniques, she was increasingly bored with school. One day an anonymous e-mail warned her that her so-called protector Heihachi Mishima was actually planning to have her assassinated, and advised her to run away as soon as possible. Guessing that the message could be from Jin, she took it to heart.
Ling became deeply suspicious of Heihachi and the Mishima Financial Empire. As if on cue, the organisation announced the upcoming King of Iron Fist Tournament 4, and Ling willingly complied with Heihachi's suggestion that she should sign up as a contestant. Ling hoped to be reunited with Jin and unravel the sinister secrets of the Mishima Financial Empire.Source: Tekken 4 Manual
