How do you prevent them? Make sure your asset can be published before moving or renaming it.
Most of the time UN-publishing is automatic when you rename and move items, but if you have set a specific asset to not allow publishing, it will NOT un-publish automatically.
How do you know if your asset is publishable? Publish it! If it is set not to publish, Cascade will alert you. If it publishes just fine, continue to move or rename it. Once the asset has been moved or renamed, you will just need to RE-publish it with its new name or in its new location.