Completed Drop Ship Purchase Orders are not purging. Found that completed date on Total tab is not populating

A client has a great deal of drop ship purchase orders that are not purging and I found out that the the system requires that the status must show completed and the completed date be populated before the purchase order can be purged. 

What step sends the complete date to the purchase order?  Receipt of Invoice that matches the quantity ordered?  

Just trying to figure this out.