Steps to reproduce:
1. Download attached project
2. Enter "SomePrefab" prefab edit mode
3. Drag reference to "SomePrefab" from Project window to the "ScriptWithAGameobjectField" component
4. Notice console prints an error
5. Exit prefab editing mode
6. Add prefab to the scene
7. Notice that game object reference still null

Expected results: Reference to itself isn't missing
Actual results: Reference to itself is missing.
Note: reentering prefab edit mode shows that reference to itself was saved.

Reproduced with: 2019.1.0a4, 2018.3.0b5

Error:
AssetImporter is referencing an asset from the previous import. This should not happen.
UnityEditor.EditorApplication:Internal_CallUpdateFunctions()