If the charging case runs out of battery, it can affect the normal use of the Redmi Buds 6 Pro.
When the charging case has no power, you will be unable to reconnect or pair the earbuds with your device. Additionally, you will not be able to restore the factory settings of the earbuds, as this requires the charging case to be powered. Furthermore, firmware updates via OTA (over-the-air) push will also be unavailable, as the earbuds need the charging case's power to perform the update.
To ensure the proper functionality of the earbuds and maintain all features, it's important to keep the charging case charged.