How to reproduce:
1. Open the attached project (case-1230444.zip) and open the SampleScene
2. Select the GameObject
3. Enter the Play Mode

Expected result: the LocalizedString 'SomeString' attached to the GameObject gets set to 'NewTable/Entry1'
Actual result: the LocalizedString 'SomeString' attached to the GameObject remains a null

Reproducible with: 0.5.0-preview (2019.3.6f1, 2020.1.0b2, 2020.2.0a5), 0.6.0-preview (2019.3.6f1, 2020.1.0b2, 2020.2.0a5), 0.6.1-preview (2019.3.6f1, 2020.1.0b2, 2020.2.0a5)
Could not test with: 2017.4.38f1, 2018.4.20f1 (package unavailable)

Workaround: the issue seems to be a bad if statement in the SerializedTableEntryReference.cs. Changing if (string.IsNullOrEmpty(keyName)) to if (!string.IsNullOrEmpty(keyName)) fixes the issue.The Script is located here: ProjectFolder\\Library\\PackageCache\\com.unity.localization@0.6.1-preview\\Editor\\UI\Tables

Notes:
1. About the project setup: the GameObject has 2 Script Components. SomeAsset.cs Script only has a LocalizedString value. Test.cs Script has a reference to the SomeAsset class and tries to set its field by calling the method SetReference. There's also A Localization String Table created which has an Entry called 'Entry1'
2. Packages 0.4.0-preview and below do not have the SerializedTableEntryReference.cs Script implemented