Understanding the Base voltage of PNP when driving NPN transistor is cut off and there is no clear DC bias voltage
If the NPN transistor is cut off, then it doesn't allow any current to flow into its collector.

Therefore there is no current flowing through the base-emitter junction of the PNP transistor.

But the I-V relationship of the b-e junction is similar to that of a diode. The only way current is zero is when the voltage is also zero. 

So the b-e voltage must also be zero in this case.

Another way to look at it is the b-e junction acts as a non-linear resistor, which is able to pull up the base voltage to equal the emitter voltage if no current is flowing through the junction.