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Some Evil Team grunts can steal your pokemon if they KO it. You have to rematch the grunt to get it back, but now it has minimum affection and friendship and has a pokerus type status called Rebellious that makes it loaf around every turn. goes away after 1 day in real time.
Legendary ghost type you can catch is your dead grandpa. Or dead grandma. Or dead Mom, depending on whether or not you want her to die during the story.
Mayfly pokemon that only lasts for 48 hours real time before it flies away to die in peace somewhere else. Instead of leveling up the pokemon, you level up your skill at training them, represented by a key item that gains levels. You can set their natures by feeding them berries and always come with perfect IVs. Ones that appear in the wild are the same level as your key item too. You better get used to going to catch them often, they don't last long.