One of my villagers told me they were planning on leaving soon. I did, however, initiate the conversation first. Click on them, and they give you a small bit of information if they're planning to leave. I didn't see this neighbor carrying special boxed and such.
well when my animal moved he would mention everyday for a awhile about how he wanted to move and then after a few days of that he had boxes in house and then he finally moved! so yes your neighbors do let you know when they are going to move.
ive only ever seen boxes when someone moves in and yes, when someone is planning on moving out they should tell you through conversation and you can sometimes say "don't go!" and sway their decision, once they've moved they should send you a letter (ive heared they dont if you've been mean to them)
pinky told me yesterday that she was moving, and i said "don't go!" but she told me that she was very sorry, but she had already made up her mind, lol. she must hate me lots...
Usually, a couple days after one animal leaves another one comes. I had benedict move out of my town like four days ago and Pippy just moved in today so it takes sometime.