How do you drain a pool and not have it pop out of the ground?

It depends on if you mean damage to the liner, the bottom or the walls. The liners go bad and shrink if not kept wet and evidentally this can happen very quickly. The walls should be held in place with braces and a concrete footer if it was installed properly and the weight of the concrete apron (sidewalk around pool should keep walls in place so these should normally be safe. The pool bottom if it is not too old is probably a mix of vermiculite adn cement from 2-4inches thick and this can be damaged if your water table is high in your area. If this is true them hopefully who ever installed pool should have put in a sump or french drains ect..to help keep water from coming up under pool and pushing the bottom up. You have to remember that at some point your pool didnt have water in it. ie during construction.