The purpose of that braided wire is to ensure that the points themselves have a path to ground. A lot of people don't realize this, but the 12 volt POSITIVE is constant to the coil (less anything the resistor brings down). It is the points opening/closing to GROUND that completes the electric circuit (and ultimately sparks the spark plug). Just crimp a connector on that wire and screw it down to the larger breaker plate.
BTW, at least the Pertronix electronic system works by the same principle. It still completes the circuit to GROUND. It just does it through electronic components rather than physically with the moving points. A lot of people get confused because the electronics of the Pertronix itself requires 12 volts POSITIVE, they incorrectly assume it is 12 volts positive that is pulsing the coil. That positive voltage IS needed to make the electronics work. BUT, the end results of its function is still to ground the coil, just like points would.
So, if that unattached braided wire is the problem the Pertronix will not necessarily cure it.