Redux state can be cached locally using IndexedDB, a type of browser storage, allowing users to preserve their input data even after page refresh. A middleware is created to trigger the cache function on specific Redux actions, and another middleware is added to delete the cache data when certain actions are triggered. By adding version numbers to the cache and setting expiration times, developers can further control the cached data. Local caching opens up new use cases for applications, such as handling large forms or caching API responses to avoid repeated calls.