Basically, when a villager moves out of your town, they kinda stay in an invisible list in your game. When you visit a town that has 10 villagers (the max amount), the invisible list clears out. If you visit a town with less than 10 villagers (or someone with an invisible list visits you when you have less than 10 villagers), a villager from the list will try to move into the town.
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So, what I'm looking for is someone who has 10 villagers in their town (and preferably isn't planning on moving any villagers out). If I visit that person, my void (invisible list) will be cleared.