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Two questions: how does a Pokemon send a rescue request when they're trapped inside a dungeon? Also, how long can a Pokemon wait to be rescued? In the games, you can take as long as you want to go to the dungeon and complete the mission, but that's probably just a video game thing. However, I feel like this could be how it works in-universe--maybe the dungeon somehow warps time and makes less time pass for the lost Pokemon, so they don't have to survive or wait for very long even if it takes a while for rescue to arrive. That's just an idea, though.