The villagers don't remember you. They treat you as if they were meeting you for the first time.
16 "cycles" is the length of time the game remembers them for after they move out of your town. After 16, the game "forgets" and their data is deleted. That's when you can move them back into your town.
Both Truffles and Pudge recently moved back into my town, ugh. D: My first Pudge moved out 17-ish villagers ago and my first Truffles moved out I think 33-ish villagers ago.