When removing an object's main location, select the object and click the locations tab. All other locations are listed, but none are set to main location.
From now on all remaining locations can be removed; you'll end up with a dangling object and ezfind stacktraces when you search for the dangling object.

Steps to reproduce

1) Create an article with several locations.
2) Remove main location using the "Remove selected" button in sub-items-list
3) Select the article and list locations within the locations-tab.