Yuchi

Yuchi is the het ship between Yuki Shoma and Machi Kuragui in the Fruits Basket fandom.

Canon
Machi is one of the few who boldly proclaimed her distaste in Yuki, or at least disagrees with the Prince Yuki Fan Club. When Yuki was not chosen as Prince for the school play, Cinderella-ish, Machi said that Yuki did not meet the requirements to be Prince. Later in the series she becomes attracted to Yuki as he tries to understand her. The two grow close as they learn more about one another. They can relate to each other as they both have endured hardships due to family issues. She even eventually meets Ayame, Yuki's older brother. Yuki understands Machi, as he understands her dislike for perfection, as shown when he breaks a new piece of chalk in one chapter. In another, he promises to make footprints in the snow with her. Yuki eventually confesses to her, when the curse broke although he had been planning to tell her about the curse. They end up dating and she is given the key to Yuki's apartment.

In Fruits Basket Another, they are revealed to be married with a son named Mutsuki between them. Machi and Yuki are a loving couple, who, according to their son, are always smiling happily together. Additionally, Machi is aware of the curse and Yuki's history as the Rat, as she was shown comforting him when he broke down in tears talking about it with Mutsuki.

Fanon
The ship sailed thanks to the two's interactions and development. Its main rival ship is Yukiru. While Machi was not introduced until later in the series, her bond with Yuki ended becoming strong and is often well-received by the fandom for being a gender-fliped example of the Brooding Boy Gentle Girl and Not So Different Tropes.

The ship became even more popular when Yuki starts to move on from his crush on Tohru as he starts to accept the fact that she and Kyo would make a better, happier couple than them, as a result, fans who went to war on who Yuki should end up with toned down and fans humbly agreed that Yuchi and him do have well-received growth.