They cannot go through the cave (yet, maybe in a sequel!). Once you finish the 16 puzzles, that particular game is done. You can start another one, try a harder game if you played on easy or normal, or just watch your villagers for a while. They do so many amazing things.
I never deleted my first game ever. Just keep checking in on them and watching them while trying to complete harder newer games.
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My VV2 story, "A Twist of Fate" And don't miss Krystal's stories, all three of them!
"Life is too fast... unless you're in traffic."