Circuit with Base of Transistor connected to ground
Take a look at this circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

Even though the base is grounded, there is still a base current flowing because of the negative power supply in the emitter loop, this is similar to what you have.

The loop equation would look like:

$$0-I_BR_B-V_{BE}-I_ER_E+V_S=0 $$

Which results in \$I_B&gt;0\$, so current does flow in this case (for proper \$-V_S\$).

$$ I_B=\dfrac{V_S-I_ER_E-V_{BE}}{R_B}$$

As long as the base-emitter is forward biased (\$V_{BE}&gt;0\$), then current will flow.