Let us assume that we have a moon with a reasonable iron core enough that it can retain atmosphere, (as per this question), now let us further assume that the people who settle on the moon are short sighted and start mining deep into the moon while also building up a breathable atmosphere. The ores are then processed and shipped off-moon to the planet.
At some point the moon is going to hit an environmental disaster wherein the mass is reduced such that atmosphere starts to leak.
How quickly would this become noticeable (assuming no one is really looking for it). Would it be gradual or sudden?
Would the planet capture all or most of the lost gasses?
What other effects are they likely to see? Would the orbit change, for example?
How much material would need to have been removed for such a "disaster" to start?