What do you call a cable that has string along with its conductors?
You frequently see microscopic conductive "ribbons" (vs. round wires) wound around non-conductive fiber cores. That is commonly called "tinsel wire" and the technique is used to make super-flexible cables that will survive orders of magnitude more flexing than ordinary wire or cable.  Very common in headphones, etc.


  Tinsel wire is produced by wrapping several strands of thin metal foil around a flexible nylon or textile core. Because the foil is very thin, the bend radius imposed on the foil is much greater than the thickness of the foil, leading to a low probability of metal fatigue. Meanwhile, the core provides high tensile strength without impairing flexibility.   https://en.wikipedia.org/wiki/Tinsel_wire