Transistor on when comparator is low

Is the op-amp being used as a comparator, or as an amplifier, or something else entirely?

It's being used as a linear amplifier I reckon and if you showed more of the circuit I think you'd find that the top of R5 goes to a positive power (or reference) rail. That positive power rail will dictate what the negative output voltage will be from the LM337.

Regulation occurs when the op-amp's inputs are equal and, because pin 3 is tied to 0V, when pin 2 attains 0V, the LM337 will be regulating.

So if the voltage at the top of R5 is +3.7 volts (pick any number really), the LM337 will output -3.7 volts.

I would not bother trying a "quick fix". I would instead try the following circuit

^{simulate this circuit – Schematic created using CircuitLab}

Basically, it requires the addition of 1 op amp and two diodes. I've shown a TL081 as the op amp, and this will work in simulation down to 1 mV or less, but it eventually runs into input offset voltage problems. If you can find an op amp with much less input offset, you can do even better. For a real circuit, get an op amp which includes an offset adjust pin, and use this to produce an op amp output of zero with zero input.

You'll also note that the comparator output is inverted with respect to the input, but that is easily remedied in logic.

EDITED TO ADD - And in the name of all that's holy, get rid of the 1N2804. It's a 50-watt zener, and is operating far below its recommended current level. A 1N4735, as shown, has a 6.2 volt rating and appropriate current levels.