What files, specifically? InDesign documents? Are they open? Can you post a screen shot of the error message?
Please don't tag onto a very old thread from2012 without it necessarily being relevant to the original discussion which was Fonts seem to install, but don't. And it had nothing to do with file deletion other than dealing with AdobeFnt cache files. For both reasons, I've branched this to a new discussion.
Please provide more information. Exactly what do you mean by “these files?” Are you talking about font files? Font cache files?
Note that if you are deleting Adobe font cache files, you will likely need administrator access for any directories you don't own if your system userid is not an administrator equivalent.