Seems like a potential nightmare when your sensor network's operation is contingent on one badly tuned power circuit in a crappy Chinese LED floodlight in the janitors closet being perpetually left on.
If there is ambient radio, you can also use that for extremely low power data transmission from your sensors. The trick there is to not actually transmit any of your own energy. You instead either absorb or reflect the ambient radio. This is called backscatter communications.
Here is a video showing a demonstration of both energy harvesting from ambient radio and backscatter data transmission [1].
If you use WiFi signals as your ambient radio for backscatter, the research group in that video has also demonstrated that you can make your backscatter data stream match standard WiFi protocols so that you can use ordinary WiFi equipment for the receiver.
The above was fairly short range, but even so there are a lot of interesting applications. For instance you might want to have moisture sensors inside a wall to detect water leaks early. If your sensors are powered by ambient EM energy (noise or radio), you don't have to limit the sensors to places where you can easily reach them later to change batteries. They are fine if they are behind brick or drywall with no openings.
If these devices can be built cheaply, just place them all over a factory, chirping their ID whenever they have enough power to do so. You map the IDs to locations and get a real-time map of where there's EM noise spitting out. When the map starts changing from it's usual patterns, then you identify the source of that change.
You Must Construct Additional Pylons