Suppose some kind of work was created long enough ago that the work itself has entered the public domain. But suppose the work has been "lost" so that it's not available anymore. Now suppose someone finds it, but the physical medium is somewhat degraded due to age, so the finder restores it so the work can be enjoyed, and perhaps transfers it to a more updated medium. Can the finder claim copyright on the restored work? Does the restored work count as a "derivative work" distinct from the original (no-longer-copyrighted) work?
The example that has made me think of this is the UCSB Cylinder Recording Archive, which makes available MP3s created from old cylinder recordings. Most of the recordings themselves are from before 1922, so they are in the public domain, but the archive has engaged in technical work to recover the sound, and they are saying you would have to pay to use their MP3s for commercial use. It seems clear that if you had the cylinder yourself you could use the recording commercially without restriction. Can a third party that made an MP3 of the cylinder impose licensing requirements on the resulting MP3?
Another example I was thinking of would be if I found, say, a lost story by Mark Twain in my attic, printed on old and perhaps water-damaged paper. If I recovered the text by looking closely at the paper and then made it available, could I impose a license on the text of Mark Twain's story (i.e., requiring people to pay me royalties to use it)?
I'm most interested in how this would work under US law, but also interested if there are variations from country to country.