FRUITS BASKET written by Natsuki Takaya starts with orphan, Tohru Honda living in a tent in the woods until she meets Yuki, Shigure, and Kyo Sohma. They invite her to live in their home, and she discovers their clan secret. The members of the Sohma family are cursed, possessed by animals from the Chinese zodiac. Whenever a member of the opposite sex not possessed by the zodiac hugs a Sohma, they change into their animal form.
This is one of my daughter's favorite anime series. So much so that after she watched the series, she read the manga online. The anime series leave you hanging at the end of the 26 episodes, plus the storyline is a bit different.
Wishing for a season 2, but there doesn't appear to be one.