When you delete a collaborated folder that you are not the owner of from your Box Sync folder on your desktop, you will receive a pop-up message that asks whether you would like to "Unsync" or "Delete" the folder. You will receive this prompt each time you remove a collaborated folder unless you check the "Always Delete" box. From that point, content will always be deleted if removed from the Box Sync folder. If you change your mind however, it is possible to reset this.
Steps to Resolve:
Uninstall and reinstall Box Sync. If you do not want to uninstall and reinstall, follow along from step 2 onward.