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Trying to find deleted (no links in the partition table) but still existing (not overwritten) files and saving them to another medium. I found that magicrescue is looking for the magic number of files and should be able to perform this task on a mounted device.
"photorec" was already mentioned, so I would like to add foremost. You can just add header and footer (and size limit) to a .conf, and search for anything you wish - easier if you're searching for non-standard file formats.