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If you exit the zone the gym is in, the gym turns into a run down, empty, abandoned building. Talking to any NPC's will tell you the previous gym leader passed away 15 years ago and left his team to his son.
His son is in the Elite four and upon defeat, mentions how it is hard to train his fathers team, as they all tend to randomly disappear from time to time.
Post game the son notices your badge and gives you a shiny gastly.