Transistor Stray pickup False Triggering Problem

The article explains how to make any BJT or mosfet based circuit free from stray signal pickup and false triggering by simply attaching a filter resistor or a capacitor across their base/emitter or gate/source terminals. The problem was raised by Mr.Henrik.

Solving a Circuit Problem

I have an issue I don’t understand. please check out the following diagram.

If I connect the Base of a PNP transistor through a 10K resistor to ground the LED lite up. If I disconnect the Base from ground the LED light up weakly. I would have expected the LED to be completely off.Can you explain me why this is the case. I have tried with other transistors also.
If I use a NPN transistor to switch a PNP transistor (Darlington) do I need a resistor from the Base of the PNP to Collector of the NPN transistor?
Thank you,Henrik

 The Reason behind the Fault:

The mentioned problem of false transistor triggering while its base was unconnected to a triggering source may be due to stray signal pickup by the transistor base causing the slight illumination on the LED.

Because as we know that when a small current flows through base emitter of a BJT, forces a relatively more stronger current to pass through collector/emitter of the device. Here too the stray signal at the base of the BJT could be forcing the device to trigger albeit fractionally, but enough to cause a faint illumination on the LED.

The Solution:

The problem could be easily remedied by adding a compensating resistor across the base emitter of the BJT, the value could be anything which allows a 1V across the base emitter when the actual trigger is connected with the base. This value could be evaluated using a resistor potential divider network calculation.

Or simply a matching value resistor could be included similar to the existing base resistor value, as done below.

Another simple way to eliminate stray pick up while its base was not associated with any form of input logic or trigger is to add a small value capacitor across its base and emitter, which would help the BJT to effectively ground any possible stray input signal and prevent it from causing the device to conduct spuriously.