The way to get the 10th villager is through the tent/igloo? Can you go to someone's town who has a boxed villager and get your 10th one that way? or will they not move and it's only the tent/igloo?
Villagers who are in boxes in other towns are able to move to your town, as long as you don't have 10 villagers - so yes, they can be your tenth villager.