How have you configured the delete to work?
Where is it getting the the file name value from?
on the delete page, you should have a record that returns the file name from the database for the record about to be deleted.
store the file name in a hidden form element that you add to the delete form. In the delete behavior, get the file name from the hidden form element.
Make sure that the delete file behavior is before the delete record behavior.
On the update page, again, add a hidden form element that captures the existing file name from the recordset. In the Upload File Behavior, set the default file field to get the value from the hidden form element. This is covered in the "How to apply Digital File Pro to DataAssist Insert and Update pages" Tutorial in the How To Section of the DFP Support page: