The LM339 spec sheet indicates the maximum negative input voltage should not be more than -0.3 volts. The schematic shows the input connected to the base of a PNP transistor with the collector at the negative supply terminal. So, it looks like if the input or base of the transistor goes more negative than about 0.7 volts relative to the negative supply point, the transistor will conduct like a diode from base to collector. Is this situation acceptable, and will the comparator work with one input equal to the negative supply (0 volts) while the other is -0.7 volts below the negative supply point?
-Bill