The mechanism you seem to be talking about sounds like the (bent metal) running eye of a wire cable snare. These snares are made from material very similar, if not identical to bicycle brake cable. (There are also tent guy line tensioners that work on the same principle, albeit in reverse.) Snares work because they are fixed to an anchor, and the victim has no hands (or no hands free/available) with which to loosen the noose, which can therefore only tighten.
Not a knot, I know, but might be of some use.
-JP