How to power an LED when a circuit isn't complete
Basically the way these circuits work is by relying on the fact that soil conducts electricity, with a resistance of a few hundred kOhm. When it gets wet, the resistance changes allowing the moisture level to be detected by measuring the resistance of the soil.

The measurement is usually achieved using an amplifier circuit which produces a voltage depending on the resistance of the soil. This can be done using an Op-Amp circuit for example, or even just biasing a BJT with the soil probe such as in the example circuit below (Source of image and circuit description here) where S1/S2 are probes in the soil, and the voltage at S1 varies with moisture level.



The LED is almost certainly not in line with the sensor, but is rather turned on or off by the measured voltage. So basically if you want an LED to have the opposite indicator, you would just need a simple inverter circuit driving the second LED.