Ground wire appears live despite not being connected on either end
Most likely it is capacitative coupling from the other conductors in the cable.

Within the cable the live, neutral and ground are physically close together and capacitance will exist between them. Even though the value wil only be 10' of picofarads per foot this can cause a voltage to develop on an open wire - the earth in your case.  Because of the low capacitance the amount of current available will be extremely low but if your tester screwdriver is a typical neon type it only needs a few microamps to cause it to glow. If you measure the voltage with a meter the voltage will drop significantly and will probably only be a few volts.

In a similar way I have seen fluorescent light tubes glowing slightly even when the power switch is off for the same reason.