I have been curious when I had first played soul silver & I now realise after starting over for fun that it is already gone by the time you have to show togepi to elm. I'm thinking Lyra might have it, but I don't know.
No one knows.....well actually during the progression of your game it sits in its pokeball,so i guess its doomed to be there for all eternity.
It's possible that he kept it, and this could be a possibility since in the beta version of Red/Blue/Green Prof. Oak can be battled and one of his Pokemon is the starter that neither you nor your rival chose. The most likely thing is that either he kept it or he released it.