Assuming that two poles stand upright. Then does this:
A rope was hung between two poles.
necessarily mean that the one end of the rope was attached to one pole and the other end of the rope was attached to the other pole? Could it also mean that the rope was situated between the two poles, but was hung on something else not mentioned?
Generally when you talk about hanging a rope "between" two objects, you mean that one end of the rope is on one object, and the other end on the other, as you initially thought. There's not much use to your proposed, more literal meaning of being hung on something between the two ropes, because it doesn't describe where exactly the ends of the rope are.
It's like asking somebody to draw a square with only two straight lines. The word "with" will generally mean "using" when you use it in that context, which makes the puzzle seem impossible. But if you interpret "with" as "alongside", suddenly you just draw a square, and then two straight lines inside it, and you've solved the riddle.
If the alternate interpretation of the word requires that much lateral thinking to come up with, then it's probably not a suitable usage of the word for everyday language.
I would say that it could mean the rope was hung on something(s) between the two poles. I would also say that the context given still seems to indicate that the rope is hung from the two poles. My preference would be to say that it was hung from two poles. That sounds accurate and proper. Like @meatie said, hung on isn't bad either.
Ropes have to hang on something (it's one of the well-known things that ropes do), so when you say this:
A rope was hung between two poles.
you strongly imply that they are on the poles, either tied to the poles directly or put on a hook on the poles.
Could it also mean that the rope was situated between the two poles, but was hung on something else not mentioned?
Why else would you mention the poles in this sentence with the rope? If there is a good answer to that due to context, then yes, but otherwise no.
A rope was hung on two poles
There's a chance someone could assume you really meant "A rope each was hung on two poles" - meaning two ropes, two poles, other end of rope on the ground. With between this wouldn't happen.
