My parents got a ceiling light for my parents for Christmas, which I was tasked with installing. I don't know why I bothered to check the voltage before putting the new fixture on (and after taking the old one off,) but I did, and it read 123V when on (good, obviously,) but it read 38V when turned off.
I disconnected all of the wires and checked the switches, and they worked perfectly fine (complete discontinuity when broken). I did break one of the switches, however, when releasing the wires that they'd stabbed in the back (20 year-old plastic is sorta brittle, I guess,) so I got new 3-way switches and not surprisingly, this did not fix the problem.
I removed the wires from the switches, except I kept the line attached to the first switch and tested the switched terminals vs. ground. I got 123V on the active terminal and <.5V on the inactive terminal -- checked out just fine. As soon as I connected the wires that lead to the box with the second switch (which was not connected,) I got 37V on the wires that were supposed to be disconnected from the line. (Actually, one reads 55V when disconnected, and the other reads 37V when disconnected.)
Unfortunately, I do not have an insulation tester, but it would seem as though the insulation has failed on those wires (assuming no stupid mistake was made by a previous installer.) However, I am open to comments about why this might be happening. Any thoughts? Anyone ever had this happen before? Etc.