Zipper cream peas are easily grown in the Southern US. They can be picked green when still immature snap beans, or when mature enough to be easily “unzipped” to release the peas. If left on the plant, they will eventually dry.
Once the peas dry, the plant will die. If continuous fresh peas are desired, pick the mature green peas (don’t allow them to dry on the plant) and peas will continue to produce—as long as environmental conditions are favorable.
Whether fresh or dried peas are harvested, compost the waste.