Steps to reproduce:

1. Open a Unity Project
2. Open the Index Manager window by going to Window > Search > Index Manager
3. Create a new Index by pressing the '+', pressing on Assets and then clicking create. Save the Asset Index with the file name TestIndex
4. In the Index Manager window (not the Project browser), rename TestIndex to TestIndexxx. Note how only the name changes but not the file path or the actual file name
5. Close the Index Manager window
6. Move the TestIndex.index file into a different folder
7. Re-open the Index Manager window by going to Window > Search > Index Manager

Actual results: The TestIndex index will be missing from the list of indexes

Expected results: The TestIndex will still be visible in the list of Indexes and will have correctly kept the reference to the .index file

Reproducible with versions: 

• 6000.0.10f1
• 2023.2.20f1
• 2022.3.36f1
• 2021.3.40f1

Not reproducible with versions: -

Can’t test with versions: -

Tested on (OS): Windows 11

Notes:

• Sometimes the Index is still visible in the Index Manager after re-opening the Index Manager. However, right-clicking on the Index and clicking 'Force Rebuild' will cause a 'FileNotFoundException' saying it could not find the file.
• Quitting the project and restarting the Unity Editor can cause the Index Manager to re-find the .index files. Performing the reproduction steps will make it lose the file again.