Outlook "Empty Deleted Items folders when exiting Outlook" option is greyed-out
Check if you have enabled the emptytrash registry key, make sure you have set its value as 0 to disable this option. If you could not find this registry key in your environment, please try to manually create the path and values like below:
Registry Path： HKEY_CURRENT_USER\software\policies\microsoft\office\16.0\outlook\preferences
Value Name： emptytrash
Value Type： REG_DWORD
Disabled Value：0
For more information: Empty the Deleted Items folder when Outlook closes.