I doubt that it was ever clarified, but, what do you think?
Due to the fact that they live in a big house, maybe the Belladonnas are a sort of royalty in Menagerie.
Ghira is called Chieftain and not president after all.
The thing is that he traveled through the world and was the former High leader of an international organization like the White fang.
Even Blake seem to went out with him, considering that we saw her in pacific protest since she was a kid.
And, it's not like it was ever mentioned about how Ghira inherited the position from his parents or something.
What's more, if the Belladonnas were the elite of the island. How? Were there already faunus in Menagerie before the Great War? The fact that at the end it was confirmed that the story of the Faunus princess was somewhat real, seem to imply the case. Though, it would be too bold to assume something from it as canon.
I doubt that she just went to an island in the corner of Remnant just to suicide, probably she already lived there.
Though, the idea of Blake being a princess don't convince me.