Negative Voltage Supply Indicator Led
I am intending to make an indicator led circuit which shows the negative 9 V supply is coming to the circuit and led becomes on, but if there is zero volts, the led will be off. 


I am understanding that you simply want an indicator to show that there is a negative voltage available.  The LED configuration below will accomplish this.  

When the source V1 reaches the Forward Voltage of the LED it will illuminate, and when V1 is 0V the LED will be off. 







simulate this circuit &ndash; Schematic created using CircuitLab

Let's look at an implementation example:

In the circuit below the +5V is DC and can be supplied from any source, i.e. a bench supply or wall wart (but an Arduino could have trouble sourcing enough current.)  

The Murata MEV1S0509SC is an isolated DC-DC Converter.  It is a switching converter that will convert +5VDC to +9VDC.  Because it is isolated it is completely acceptable to connect the positive output to ground and use the negative output as shown.



Now for the LED.  I picked an HLMP-3301 which has a forward voltage of 1.9V typical.  A diodes forward voltage is the voltage required for current to flow.  Sparkfun has a good artical about it here: Sparkfun - Diodes. 



Operation:  When -Vout is "ON" (less than 1.9V below ground) the LED will have a forward voltage applied (0v - -Vout) and the LED will illuminate.  The resistor is there to limit the current through the LED so it doesn't burn up.  In this example, I picked a 10mA current at -9V Vout.