Transitor keeps base turned on even at zero volts in dual power supply system
Anatomy of a half-fried transistor.

Imax=50mA @ Vce=0.12V at 25'C on a heatsink
Ipk=100mA  ( short pulse)
Vce(sat) is defined using Ic/Ib=10 for switch mode which or practical design use 10% of max hFE.  Motorola used to call this base over drive factor.

If metallization migrates (contaminates) into semiconductor region it becomes a partial conductor so that it starts conducting with strange non-linear + linear current at lower voltage.  Eventually it shorts out CE junction.

Unfortunately since diodes have a Neg Temp coefficient, the Vbe vs Ibe which appears to have a high Ohm bulk resistance,  rises in current with  Vbe voltage and generates heat in Vbe so as it gets hotter  then threshold temp drops even faster leading to a possible thermal runaway with a 0 ohm voltage source.  







simulate this circuit &ndash; Schematic created using CircuitLab

The forward voltage of a Si diode will drop by about 2.1 mV/°C (negative temperature coefficient, NTC) so if junction has risen 100'C Vbe drops 210mV so with 20 Ohms base resistance at Vbe=900mV now what is your base current? 

Its a moving target as assumed temp keeps rising and depends how long you run it for.

Which is why you tested the device incorrectly leading to thermal failure by not using a 500 Ohm base R and 50 Ohm Collector to measure hfe saturation vs I.  

see Vbe=0.8Vmax at 10mA with Vcb=5V meaning Vce=4.2V and linear hFE is 130 min @ Ic=2mA so Ib could be 10m/130 or less or 0.8mA thus bulk resistance above 0.6V is 200mV/10mA=20 Ohms but as 0.6V threshold drops with temp to 0.5V now the base current rises with T.

Now you are little wiser about reading datasheet specs and consequences of ignoring them.

Advice: consider temp rise at rated continuous current will be at 85'C with ambient cooling or more.

YOu should have stayed with just one 100 Ohm collector resistor and used 10 Ohm base resistor to measure current.