In some cases you are forced to hard-remove public folders from Exchange. You can use ADSI Edit to delete these folders.
Open ADSI-Edit and got to configuration
Navigate to this path:
CN=Exchange Administrative Group (FYDIBOHF23SPDLT)
Now you can delete the PF-Database you want to get rid off.
CN=First administrative Group
Super..Excellent..!!! Keep going:)
Excellent its very helpful...!!!
But want to highlight one more thing. Once you delete the Public folder database directly from adsiedit then there are many entries in adsiedit which will point to "Deleted objects" like sitefolderserver.
Also mention to correct those settings