Answering your question should really begin with a short course in electrical theory and circuit design. Knowing a few of our more prolific typists on this forum, you may get some of that.
The effect you're noticing is a by-product of the design of most basic solid-state power amplifiers. It's all about volts. They attempt to output a specific voltage gain that is a function of the input voltage. Most amplifiers have a constant gain of between 26db and 32db. So if the input voltage is 1.0 volts, the voltage at the speaker terminals if the amp has 26db of gain will be about 20 volts. The power amp gain is always constant, the input voltage just varies depending on the source material and the position of the volume control on the pre-amp.
If the power amp is perfect, and no amp is, the amp would output 20 volts regardless of the impedance of the load. If the impedance drops the power must increase to maintain the same voltage level, roughly analogous to how more water must flow through a pipe to keep the water pressure constant as the pipe diameter increases. Using Ohm's Law to calculate power, 20 volts into an 8 ohm load is 50 watts. A perfect amp would output the same 20 volts into 4 ohm loads and 2 ohm loads, and the output would be 100 watts into 4 ohms and 200 watts into 2 ohms loads. Most amps aren't perfect, so their output voltage drops considerably as impedance drops.
The ways amplifiers work is that their power draw from the wall outlet is mostly dependent on the load the amplifier is driving, so it will draw less power when driving 8 ohm loads than 4 ohm loads. This is one reason why low impedance loads are called "demanding". They demand a more capable power supply in the amplifier, not to mention more capable output circuits. There isn't any "missing" power; the power draw is simply a function of the demand, which is a function of the load. It appears to work automatically, but it's really just a matter of physics and circuit design.
I've highly simplified everything here, and the way a speaker loads an amplifier is much more complex with more factors than I've described. Also, some solid state amplifiers, like those from McIntosh, for example, don't work this way. But hopefully this gives you some clue about the answers to your questions.
