Beginning with version 4.5 you can query empty fields via Search API, as documented here:
https://developer.enaio.org/display/DD/Search Service API
"basisdocument.status": {
"o": "eq",
"v1": null // for any field: This query returns documents that have no value in the named field.
},
The search for empty fields is also support by using search forms in the search dialog of the client. A click onto the field label signals search for an missing value.