Pokemon Ranger: Guardian Signs
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The egg event only occurred for a short time after the game was released. It is possible of course to find a preowned game where they got the event and didn't complete it(I found the manaphy and shaymin event that way.) But it's super unlikely since most of these games are over a decade old.
Considering that it is extremely difficult to find those games in new condition I doubt that it would have the original case. The games would still come with one but it would not be specific to the game.