sounds like a switched neutral to me. i just dealt with one this weekend at my parents house. I dont do residential so this type of ****ery had my head spinning. with the switch on i got my normal 110, with the switch off i got 56V.
it wasnt a 3-way though, but im sure they switched the neutral somewhere just like in my case
did you try testing Hot to ground, and Neutral to ground?
it wasnt a 3-way though, but im sure they switched the neutral somewhere just like in my case
did you try testing Hot to ground, and Neutral to ground?