Yes, carnivorous plants can survive in a closed terrarium. To create a successful terrarium environment for carnivorous plants, the terrarium must contain an abundance of water, sun, and high relative humidity.
Be sure to use a terrarium that is large enough for the plant‘s root system and take care to provide extra ventilation by placing the terrarium lid slightly ajar. Additionally, carnivorous plants need to be fertilized with special fertilizers or nutrient–free water to help them thrive in a terrarium environment.