Petitioner: Chen Linxi
Important note: Until you trigger this quest you can continue to Invite Chen Linxi in your party, and he'll stick around and help you out. Once you speak to him, however, there's a chance he will be permanently removed from the party. If you have an Affinity above 70 with Linxi and want to keep him as a party member you should not do this quest. Just click 'Observe' and 'Invite' to recruit him, and never speak to him again.
After 'solving' the case of the frozen corpses in Beishan Village, Chen Linxi will leave the party and return to Pingkang City. If you follow him back you'll find him in his Martial Club, though his two disciples seem to have disappeared. Linxi is nevertheless cordial to Yi, and suggests sitting down for some drinks.
Head to the inn and speak to Sai Jinhua, the woman behind the front desk. She'll give you two Snowball Nectars. On your way out of the inn you'll hear that Linxi plans to close the Martial Club, and hasn't been seen for a while. Odd.
Save your game, then return to the Martial Club. A cut scene triggers, and if you have an Affinity with Linxi that's below 70, and you didn't defend him in the previous quest, things will resolve peacefully. You can continue to use Linxi as a party member, and you'll receive the Wintry Blow and Thunderous Palm Strike manuals, as well as Martial Arts Perceptions. If your Affinity is above 70, however...
Chen Linxi
It turns out that Linxi didn't take his defeat to Yi lightly, and now he wants to settle the score. He fights the same way as during your first brawl, albeit a little stronger. Expect lots of close-range melee hits and the occasional Frosty Palm Strike. Stay on his flanks and heal as necessary.
You'll receive the Wintry Blow manual, the Thunderous Palm Strike manual, and another piece of equipment for defeating Chen Linxi. The quest ends with Zhan Wuxing cleaning up after you, and Linxi is gone for good. Well, that sucks, doesn't it?
(Slight confession: I haven't had a chance to fully test this. I didn't find out about Linxi's death until I hit this quest, and I didn't have saves or autosaves going far enough back to lower his Affinity. I've seen a video which shows him surviving this quest, however, so... when I get the chance I'll replay Wandering Sword and try this again for verification.)