Are found media saved so that they don't get lost again?

What you guys can always do is that you can download said video from YouTube, and then upload it to the web archive at archive.org. You'll need to make an account to upload, but unlike YouTube, it's MUCH less likely to get taken down through copyright, though it still does happen.

I remember I had uploaded two episodes of Audrey Hepburn's Gardens of the World to archive.org, but the unfortunate thing that happened there was that the producing agency apparently still cared about the work (something that wasn't entirely obvious like uploading a movie in full), and got in touch with the site to take the episodes down. On the bright side, unless your uploads are absolutely blatant breaches of copyright (such us uploading any movie made since 1970), your account will not face any penalties for them.

I've uploaded over 600 items to the site, most of which is copyright material in the technical sense, but a lot of stuff is considered "abandonware" where it's still legally under copyright, but the agency that owns the copyright won't go after the uploader because of the irrelevance of said uploaded item. A lot of lost shows and other materials (not all of course) work in a similar fashion though.