Hi,
you can create a menu item with only users with this field empty. for example if your field have alias like "test_field" you can put this into Custom SQL Where parameter in menu item options:
test_field=''
Strange that you can search on any letter in or parts of words, but not empty field.
This is a only way, for example if I have a form with Name and City then I can search for Name,City,Name and City. If you not fill search criteria the system ignore this field.