Dear student,
Cuscuta is a parasitic plant and survives even without leaves and chlorophyll. This is because parasitic plants are those plants that use parasitic mode of nutrition which is a mode of heterotropic nutrition where a parasitic organism lives on the suface or inside the body of the host organism and derives nutrition directly from the body of the host.
Hence cuscuta plants survive even without leaves and chlorophyll as they do not need to prepare their own food unlike green plants that require leaves and chlorophyll to make their own food.
Thanks and regards.