Lokoko

Lokoko is a character of the day from Ep 234 Lokoko lived in a mansion with a Kyukon. Takeshi fell in love with her, and was considering living with her forever. However, Satoshi and Kasumi felt that something was odd. Whenever Lokoko went by a mirror, she had no reflection, and whenever they tried to alert Brock to what was happening, Lokoko and Kyukon would get in their way. After finding an old room in the mansion, they learned that the Kyukon belonged to the owner of the mansion. He left one day hundreds of years before, and never returned. Lokoko was an illusion created by the Kyukon. After a battle with Team Rocket, Takeshi learned the truth about Lokoko and Kyukon.

The reason they wanted him to stay was due to his resemblance to the mansion's owner. After Kyukon's Poké Ball was broken in battle, Takeshi told it to go free. Once it did, the mansion and Lokoko disappeared.

(Source: Bulbapedia)