So do you still have to cycle through x amount of villagers before you can move in a Villager that left?
How does that work with amiibo cards, I assume you can move them in multiple times?
I'm not very exactly sure about your question, but, let's say Tia left your town. You'll need to cycle 16 out in order to adopt Tia through adoption from other's town. But if through amiibo card, you scan Tia's card, then she'll be moving in the next day regardless of the number of villagers that have left after her.
And, it's not zero chance but she most likely to not move out again, unless 8 out of 10 villagers in your town are through amiibo scan-ins. If that's the case she'll move out naturally at some point. And if not the case then you need to kick her out by scanning in other villager. Once she's kicked out that way, yes you can scan her in again to let her move in your town, no need to worry about 16 cycling.