In S2EP5, Plum is actually named Zeta, but due to very weak health she died when Kairo was young and she was erased from his memories.
As Zeta Edit
Throughout the series, she only appears in Sun-Hi's dreams. Eventually, Zeta reveals that she created Plum: the pet who died 4 years ago and the pet who grew up with Kairo was a clone she made so that he would not forget her. Zeta is actually the real Plum!