Hey there,
I'm going to assume you are referring to our Firebase Hosting product. When you do a Firebase deploy, we do send all of your project files (except those which you tell us to ignore in your firebase.json file) and store them. However, we do not provide a service for retrieving/cloning old versions of your site. We do allow you to roll back to a previous version, but we won't actually send you the file list. You should use git or Mercurial to store those files yourself, instead of relying on us to do that.
If you are not referring to Firebase Hosting and instead are referring to Firebase data itself, you can export your data either via the REST API or from your Firebase dashboard.
Jacob