In the prologue in The City and the Stars by Arthur C. Clarke, it reads
Since the city was built, the oceans of Earth had passed away and the desert had encompassed all the globe. The last mountains had been ground to dust by the winds and the rain, and the world was too weary to bring forth more. The city did not care; Earth itself could crumble and Diaspar would still protect the children of its makers, bearing them and their treasures safely down the stream of time.
They had lived in the same city, had walked the same miraculously unchanging streets, while more than a billion years had worn away.
Now, with Lys being still alive, and all the things that Alvin and Hilvar see, the planet is not in as dire a state as the prologue says, but what would happen to Diaspar if it was? If the Earth, over time, did crumble away into dust, would Diaspar be all that was left? Would it just be a floating bubble in the universe? It's built on Earth, so does Diaspar actually need Earth to survive?
In universe answers, if possible, please. I refuse to believe anyone who says that Arthur C. Clarke didn't think it through and that it's a hole in the story.