Can previous villagers from Animal Crossing: New Leaf move back in?

This FAQ on Reddit specifically around New Leaf says:

After you’ve had 4 villagers move out, the 16 most recent villagers to have left your town have the chance to show up on main street to do a little shopping every day. They just miss you! If you don’t want them there, get 16 more villagers to move out and the one you don’t like will be gone. This is also a good indicator of whether an old villager can move back into your town or not. The moment they stop appearing on main street, they’ll have cleared the 16 villager cycle and will be able to move back in to your town.

Now about moving in, I do know that you cannot convince then to move back even if you see them shopping about. You'll have to get them by random chance again or find the desired villager in a friend's town who is moving out.

Well when you think about it, yes old villages can move back in.

They will move back in if you do the following:
First, you should ignore all the villagers in your town for two weeks.
Don't do it to your to favorite currently there if you have two. Soon they will move out.

Secondly, a bunch more will move in.
Don't greet them if it isn't the one you are looking for. Then if he/she doesn't come, don't talk to any of them for two weeks.

Thirdly, once all of the others move out (other than two favorites) then see if you have the one your looking for.
If you don't, don't even stop to greet any until they move out.

It might take a couple months, but it will work!
If it doesn't work after 4 months then you may just be unlucky.

Note: If you had updated data during that time, there is a chance they deleted that villager. Hope you get your villager!

Think about it, There's only a certain amount of villagers in animal crossing, right? http://acwiki3ds.wikispaces.com/Villagers

once you've seen all of them, the old ones..they'll have to move back in.

They may visit the campsite

, if you have it. Lyman recently left my town and he was my favorite, I'm currently holding for him to come to my campsite! Good luck on getting a chief back!! ??

Get the campsite; they'll show up at least once. When they do, talk to them a lot. Sooner or later, they'll bring up moving into town, and say, "if you beat me in this game, I'll move in". Accept the challenge, then try to win. If you don't, you have to give them something. If you do win, then they'll move into town the next day.