How to reproduce:
1. Open the attached "1270634 repro" project
2. Extract files from "TheMissingFiles.zip" archive to the Assets folder of the project
3. Focus the Editor and select the "GameObject.prefab" Prefab from the Assets folder

Expected results: the "Object Custom Object" reference targets the "MyCustomObject.asset" file
Actual results: the "Object Custom Object" reference is set to "None (Custom Object)" and reimport of the Prefab is required

Reproducible with: 2018.4.26f1, 2019.4.9f1, 2020.1.5f1, 2020.2.0b2

Notes:
-This scenario is most likely to occur when using Version Control
-This issue reproduces with ScriptableObject and Timeline references
-This issue doesn't seem to be reproducible with missing Sprite, Shader, Audio Mixer, Controller, Terrain Layer, Physics Material references
-When a reference witch reproduces the issue is missing, the "Object Custom Object" field displays "None (Custom Object)"
-When a reference which doesn't reproduce the issue is missing, the "Object Custom Object" field displays "Missing(Sprite)"