Historically, stateful workloads were run outside container orchestrators. Platforms built on top of orchestrators like Kubernetes were not, yet, proficient at dealing with data. But these systems have matured and now offer features the allow stateful workloads to be efficiently managed by such systems.
If you want to find how can databases be run on Kubernetes, what mechanisms it offers, and what type of databases and data are best suited for it, check this out.