Same thing that happens to every leftover starter pokemon:
Dorkly Bits: The Horrible Secret Behind Starter Pokemon - Dorkly Video
"Strong Pokémon. Weak Pokémon. That is only the selfish perception of people. Truly skilled Trainers should try to win with the Pokémon they love best". -Karen
"For every pokemon there is a purpose and a time when it can shine under the sun." -Blue1225
Given away to another ten year old, I guess.
Maybe Crystal is running around with it off screen? That's what I am going to go with as I am miffed over her being retconned out.
The in game description gave us mystery so we would be discussing it like now. We will probably never know.
"I don't know where I am. I don't know where I'm going or where I've been. I was born to save the Doctor. But the Doctor is safe now. I'm the impossible girl, and my story is done."
It's still there even after I beat the E4, so maybe the prof is just keeping it
maybe it was given to the opposite gender player character that becomes the professors daughter
There was unused trainer data in Red and Blue for Oak when he had the third starter. So I always thought that whoever the Prof. of the area was, took the pokemon.
I always imagined that in HG/SS, Kris got the Pokémon. Maybe in G/S/C, Lyra or Gold (Ethan) got the other.
Crazy stuff, ya know.
Or Prof. Elm just went back to Fiore and released it. 'Cause that's where Prof. Oak, Elm and Birch get the starters from.