There is no mystery there.
Most opamps use class AB output drivers. This lets them give you a bigger maximum output current and low quiescent current in the same opamp. To force an opamp into class A, all you have to do is pull its output to either the + or - rail with a constant current source. The voltage feedback forces the output to stay at the same voltage, so the only way this can happen is if the opposite-polarity output transistor conducts that current into the constant current load all the time. The active internal transistor is always on, so the opamp is operating class A into a constant current load.
This is major cool - if you can hear the difference. Unfortunately, this mod is nearly always followed by a description of how the mod gives an clarity, an inner piecefulness and a zen-like crystalline quality to the sound. I'm sure that there are people somewhere that can hear that in good listening conditions.
I'm not sure that there are people anywhere that could hear it when its used in a distortion pedal.
It also increases the power supply current to the opamp by the constant current load amount, and the power dissipated by the opamp by the current load times one power supply. It also thermally unbalances the opamp's output. In a modern opamp, the layout of the chip is done to equalize thermal effects as well to get greater accuracy inside. The output transistors are placed carefully so their thermal load balance across the chip and it all heats evenly. This generally relies on the output transistors heating equally. In the constant current load Class A setup, half the dissipation is on the chip, and half is off, in the external load. So some of the layout accuracy is lost.
The class A action is also only true for load currents less than the external load. What the external load actually does is move the AB crossover point away from the middle. At currents bigger than the external load, you still do crossover to the opposite side driver.
