I preserve old software by asking copyright owners (often one author) to release the source code under an Open Source License, GPL or MIT. In many cases the source is gone, but the binaries still exist. Often they were released under some home made license 20 years ago. If I'm correct the binaries could be released under MIT, which would give them a world wide recognized license, keeping the copyright owner, but also make it possible to do derived works for the user in clear legal way? (I know that much of this would fall under "abandonware" but that is not a legal term). So the question is - is MIT a correct choice for binaries where the source code is lost?
In every jurisdiction I know, the author or copyright holder of a software can pick whatever license they like, source code available or not. And nowhere in the MIT license does the term "source code" occur, so the answer is clearly yes.
However, make sure you are really talking to the person(s) who have the full copyrights for the program in stake, as mentioned @BerinLoritsch.