Question: what happens to the quagmires in the books?
Answer: After being trapped inside of a giant bird-shaped fountain by the Village of Fowl Devotees and sneaking Isadora's poetry into the world so that the Baudelaires could find them, the Quagmires are whisked away in a makeshift airship (made of a hot-air balloon and mobile home) by the Baudelaires' friend Hector.