what happened?

Wow, I'm three years late ^^" From what I recall, as it has been years since I watched this, they were indeed living on the moon, with the machinery in the upper layers slowly deteriorating. That spaceship was indeed a migration ship (probably), and the grandmother of the girl presumably discovered the same thing as our main character - namely that Earth is inhabitable again. The really depressing part is that no one will probably ever know: if it would still be possible to find it out it won't be for long, because everything is falling apart and no one can repair or create anything, and everyone has become too apathetic to care. In other words, everyone living on the moon is most probably doomed.