Deleting vs Unsyncing

When you delete a collaborated folder, that folder is permanently deleted from every collaborator's account.

When you unsync a collaborated folder, you are only removing it from your computer ﹣ it remains in the parent folder and all other collaborators continue to have access to that folder. This action must be taken from the Box web application. 

See here for more details: Using Box Sync: Deleting Synced Folders