Saving/renaming a project and preview files
If you rename a project it continues to link to the old preview files. Any new preview files Premiere creates are saved in a new folder with the updated project name. So you'd be using media from two different folders at that point.

If you delete the old preview files then Premiere will just re-render them when needed.

I tested this by creating a project called test, adding some clips and applying effects and rendering. Render files were created on my scratch disk in a folder called test.PRV. Then I saved the project as test-rename. When I closed and reopened it the clips I had rendered still had the green bar above them, and played back fine, though at this point there was no test-rename.PRV folder in my preview folders.

If I moved the original render file from the test.PRV folder and re-opened the test-rename project the bar went red. When I rendered it the resulting file was saved in a new test-rename.PRV folder. QED.

Note that Premiere gets confused if you remove the render files while the project is open. It doesn't realise that the preview files are missing, and behaves erratically.