you zero all the QTY ordered, and mark all lines as complete.  make sure they are not deleting all the lines as there must be at least 1 COMPLETE line to consider the order complete.  Also, make sure the order is still set to ACTIVE and not changed to a quote or something.

Thanks Mike - that’s what they’ve been doing.  But even after they zero out all lines, check the box for Complete, Post, and Day End, the Complete status of the order header is still 2 and it still shows up on certain reports.  

maybe the reports are wrong.  you don't even need it to go through day end.  I'm betting the report is looking for at least 1  shipment/invoice number to consider itself complete.

You could test this theory but using the "set criteria" on the order entry search.  Set it to only show orders that have a completed status of 1 or 2 (which are the "not complete" ones in the drop down).  Then see if your order number still shows in that list.   If not, then you know the order was completed properly.  if it still shows, then something is still there such as a MISC item.