op-amp comparator 0 or 12V output
If you look at the schematic in the datasheet for the LM306, you will find that pin 1 (not shown in your schematic) is Ground, and the output transistor will pull the output close to Ground.  The 2K2 resistor is required to pull the output up to +12 V.  Like most comparators, the output is "open collector" - the chip can only pull the output to Ground when low.  It just "lets go" of the output pin when it should be high.

The negative power input is only used in the input stage.