I think it would be kinda cute if villagers who moved away from your town could write letters to you once in a while if you reached a certain friendship level with them. So if you were best friends and they moved, they could send you a letter telling you about their new town or things they've done, and maybe you could write back to them? Possibly there could be special dialogue that indicates you could do this, maybe when the villager is in boxes they could say something like "I'll make sure to write to you when I can, make sure you write back!" etc.