Sometime in the far future, the Earth gets destroyed. Before the Earth is destroyed, humans formed a small colony on the Moon which is capable of self-sustaining itself for the next decade or so. What would be the most logical, physics-obeying situation that would happen to the civilisation on the Moon?
It depends on how the earth is destroyed
Consider three scenarios.
The surface of the earth is destroyed. Nanites, nuclear bombs, plagues, something kills everything on the surface of the earth. The moon and the earth will just keep orbiting the sun, and it doesn't care what happened to humans.
The earth is exploded equally in all directions. The kinetic energy of the moon is about 10000 times smaller than the binding energy of the earth so the moon is probably massively damaged and de-orbited.
The earth is de-orbited and flung into the sun. The earth has even more kinetic energy than binding energy, so this is also catastrophic for the moon.
As such, the only safe destruction is 1. The earth's surface is damaged and all Earthbound humanity destroyed, but it remains a big rock that's going around the sun. If you are fine with everyone on the moon dying, 2 or 3 is fine.