There is an even more ridiculous / confusing version: one could point a kind of telescope to a really dark part of sky. Here the radiation temperature is really low, well below ambient and thus very little IR light comes from there. So an IR sensitive photodiode would show a reverse voltage (other polarity than with normal light), as there is IR radiation send to the sky with no return. So you could generate power from sending out radiation to a cold place.
I have not done the numbers but I would expect less than a bee's ...
This isn't as bad as it sounds!
But it will be thermal in nature.
You could build a moderately effective solar-thermal array by doing...
1. Build a radiator. Assuming clear skies overall, then: during the day, it will absorb sunlight and heat up. During the night, it will cool down.
2. During the day, pump the heat into a holding tank. Preferably phase change (paraffin or molten salt) storage.
3. At night, run a heat engine from the tank, using the radiator as the cold side.
This boosts efficiency because the radiator goes down quite cool at night: perhaps 40 degrees below ambient.
The heat transfer rate is fairly low, so you will need quite a lot of radiator, of course. But it will still perform better (higher Carnot efficiency) even if the radiator isn't much below ambient temperatures -- because, if you used convection cooling to ambient air instead, you can only ever have the heatsink somewhat hotter than ambient, never equal or below.
Probably, the solar array should be a concentrator type, like the trench or tower kind. The Sun is highly directional, so it's a big net win to thermally isolate your hot side from anything that's not line-of-sight with the Sun. That way you can get really hot fluid coming out. (As opposed to a flat thermal field, like say, a blacktop parking lot with thermal pipes underneath, which loses heat as radiation in all directions, plus convection off the huge area of air it's in contact with.)
Conversely, the cooling radiator should be exactly the opposite kind: because, at night (cloudless), the whole sky is largely quite cool, and you need to maximize area because the temperature is low and radiation has crappy conductivity at low temperatures.
Okay so I lied, it's not as exciting as when I started typing... The reason the collector and radiator must be asymmetrical is because the radiation source and sink are asymmetrical in nature. So, unfortunately, there's no easy two-for-one sale on that.
Tim