While the Ministry of Magic was running around trying to catch Death Eaters (during either the first or second wizarding war), did they ever capture House-Elves of known Death Eaters and interrogate them?
Obviously, the elves wouldn't reveal their secrets, but it's not impossible to look into their minds. For example, Dobby would've been a good elf to interrogate about whether or not Lucius Malfoy was truly under the control of Lord Voldemort or not.
So, unless I've missed something important, would it be possible?
They do say in the books that house-elf magic is different from normal magic, and that some of the same rules don't apply to them. So it stands to reason that perhaps the normal methods of getting into someone's mind might not work on house-elves.
It could also be that since house-elves are considered subhuman, it didn't occur to anyone to bother with it. After all, Dumbledore, Hermione, etc. were in the minority when it came to the treatment and their opinions of house-elves.