Hi Tt_nguyen
welcome rto the Apple (user-0to-user) Community.
Re: "Airpods pro 2 case is out of battery : the airpods does not work too even it is fully charge.
... when case is dead (out of battery) then airpod not supposed to work too ?"
Seems the charging case should hold multiple charges before it needs to be recharged.
The airPods should connect with your device if they are well-charged.
Apple Support has articles online to guide users in charging, troubleshooting & etc
You might want to reset your AirPods:
How to reset your AirPods and AirPods Pro - Apple Support
Make sure nothing (a speck of dirt or wax) is blocking :
How to clean your AirPods, AirPods Pro, AirPods Max, and EarPods - Apple Support
To keep your AirPods charged, put them in the case when you're not using them.
Charge your AirPods and learn about battery life - Apple Support
What to do: If your AirPods won’t charge - Apple Support
or
If your AirPods won't connect - Apple Support
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If you still need help: You might want to check if the AirPods are under warranty
How to: Find the serial number of your AirPods - Apple Support
Where to enter the serial number to see what support info. is available:
Check Your Service and Support Coverage - Apple Support
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Resource:
AirPods User Guide - Apple Support
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More Support if needed:
AirPods Support Website:
Find all the topics, resources, and contact options you need for your AirPods....
AirPods Support - Official Apple Support
All the best :-)