They can survive, but they'll grow very slowly. Most carnivorous plants live in bogs and wetlands. To be called a bog, an area must have sphagnum moss and water of a specific acidity. Bogs are usually fed by rainwater only. No in-flowing streams or underground springs bring in outside nutrients.
Many carnivorous plants grow alongside streams, or in other areas that are consistently moist.
If the ground does dry out, some plant species become dormant - they hibernate, in effect. Or, the parent plant may produce seeds and die. When weather conditions are favorable again, the seeds grow into new plants. Ill. He takes his science classes on field trips every year to see carnivorous plants. Hinkley has found small clumps of pitcher plants in Volo Bog.