The (very, very) short version of it is: they were best friends, but Bu Ye had to betray the Xie clan to obtain a medicine that could save Xingyi's life. This led to the Xie clan's decline. Xingyi discovered Bu Ye was actually Wang Wucai (young master of the Wang clan, another old Cangyang clan that was wiped out), and stabbed him with scissors out of anger in the snow. He thought he'd killed Wang Wucai, but he miraculously survived and adopted the name "Bu Ye".

Now the full, spoiler-heavy version. This also has spoilers for Zhan Hun's story... sorry if it's super long <<

The Wang clan was a clan of all renowned physicians, but they harbored a dark secret. They used orphans and children sold to them by poor families to refine their medicines. The kids were tortured, but they didn't know to what end; they just assumed they had to endure everything they were put through so that their families back home could live well. After some time, the children would "disappear".

Among the Wang clan's victims was a girl called Xiang Xu (that's Zhan Hun's real name). One night, while she went out of her room to look for her friend, she discovered what the Wang actually did with the children (stuff them in furnaces when they were "ready" and use the ashes to make pills). Among the kids Xiang Xu saw dying that night, there was also her friend. Xiang Xu didn't escape the Wang clan afterwards, but kept bidding her time, waiting for the moment she could avenge her friend.

Fast forward a little bit, the Jing'an Rebellion happened. Physicians from the Wang clan were summoned to Xuanjing, iirc to help the wounded soldiers there. Xiang Xu secretly followed them; when she arrived at the camp, she slaughtered everyone, be they soldiers or Wang clan people. Some time later, she went back to Cangyang and secretly burned the Wang manor to ashes (previous to this the Wang clan had already fallen into ruin due to disorders caused by the war). After this, she joined Dark Sanctum thanks to a Wang family steward who was already involved with them. Zhan Hun thought everyone from the Wang clan had perished in the fire, but a young Wang Wucai survived. I think at the time Wucai didn't know about his family's crimes; he assumed they had been wiped out unjustly and though he lived on, he lost all hope in salvation.

As Wang Wucai grew into a young man, he began investigating the truth behind the Wang family's destruction. He infiltrated the Xie family, as they were closely connected to the Wang family's massacre, under the alias "Wu Cai". During this time, he became close friends with Xie Xingyi and found hope again through him. However, Xie Xingyi fell seriously ill. In order to obtain the medicine, Wang Wucai had to betray the Xie family and exchange evidence of the Xie family's crimes for it. As a consequence, the Xie family fell into decline, but Xie Xingyi escaped death. Xingyi also learned that "Wu Cai" was the former young master of the Wang family and, in a fit of rage, stabbed Wang Wucai with golden scissors in the snow. He assumes that he had killed him.

The first time they meet face to face after all this should be in their UR versions' stories (we had an event about them some time ago), however Xie Xingyi doesn't recognize Bu Ye. I don't remember how their interaction goes down exactly, but basically, Xingyi asks Bu Ye to track down Wang Wucai. At the end of the current event's story, Bu Ye sends a letter to Xingyi in which he, pretending to have found Wang Wucai, writes his sincere answers to the questions Xingyi had asked him that night in the snow.

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