Kubernetes can manage stateful applications using StatefulSets. StatefulSets ensure each Pod in the StatefulSet gets a persistent unique network identity, stable storage, and ordered deployment and scaling. When a Pod is removed from the StatefulSet through scaling in, its PersistentVolumeClaim and PersistentVolume are retained and not deleted so they can be mounted by new Pods. This allows each Pod's stateful data to persist independently of the Pod's lifetime.