An FYI administrator can delete a cabinet. Refer to Removing a Cabinet in Managing Cabinets.
If you try to delete a cabinet has been set as a default cabinet for a client, you will see the message "You cannot delete a cabinet that is assigned to a client". This also shows the relevant client(s).
Change the default Cabinet for the relevant client(s) in the Clients - Details tab. Refer to in Setting Filing Defaults for a Client. You can either change or remove the assigned cabinet for the Client(s).
Check if any Documents are filed under a Cabinet before Deleting
If you delete a Cabinet that documents have been filed under, those documents will show without a Cabinet selected.
Before deleting a Cabinet, run a search to check if there are documents filing under that Cabinet.