If the island fell at the beginning of the game for some reason... Perhaps the island would be in a pretty bad state. I'm picturing Egg Corridor after its disaster, except for many parts of the island. The game would probably flow differently as well... Quote might be focused on finding and rescuing characters in new ways. Maybe there would be more Mimigas still at the village as well? Assuming something changed the course of the Doctor's plans enough to bring down the island.
Would Ballos still be sealed? If there is no main Core keeping the place afloat or if something happened to it, how much flooding would have occurred in the Labyrinth or surrounding areas? How much of the waterway will have changed? Perhaps the Doctor will need a new base of operations, depending on the state of the Throne Room area? The helicopter would likely be gone or totaled...
And where did the island crash? In the middle of the ocean? In the same spot? Near some populated area? How fast would outside forces react to the island's new circumstance, would they know?
Its up to your imagination!
What if Toroko or Misery hadn't been there when Quote met Balrog for the first time? Perhaps no battle would have taken place, and you return with Balrog to meet the Doctor? Perhaps Quote/the Player would even perform missions for the Doctor if not antagonized. The place is a wreck and The Doctor needs help getting things back on track. Balrog brings back Quote who is basically a blank slate, and who knows what strange new universe you'll end up in if you follow your imagination

The island is being invaded by the surface! Help the Doctor hold back the invaders!