Mack sorry nobody helping hya but we're not quite sure which wire is doing what. If B and C were braided together we might suppose one is neutral and the other is ground. However usu the ground is connected to the body of a switch, so we might conclude that A is the hot wire. Still you later go on to assert, "C was live," leaving us in a sort of quandary
But you go on to say that measurement showed "one of the braided wires registered a current," so we would wonder if you were actually measuring a current or a voltage. If a current, you must have disconnected the tie and measuring the current between the two, further confirming the notion that one is ground and other neutral; since a slight voltage would usu be found on neutral
So Your first two paras are prefectly clear but then if you were really measuring between B and C, then either one
would register a current. So some of us conclude by "current" you must mean "voltage."
Finally if you found "C was live," and if by "live" you mean showed a high voltage,then you must have first disconnected it from B, which raises the q as to which wire, A or B, you were measuring it with respect to
Thus if you could provide some clarifying detail we might be able to advise you; tho most others here will recommend an electrician, however prohibitively expensive. No offense ack but please don't electrocute yourself