So when you hook up a sub this way, the amp has no extra load on it? What happens to the amplified signal once it gets to the high level input?
That is correct with respect to most or all of the REL subwoofers, when their high level inputs are used. I wouldn't necessarily generalize to other designs.
When the amplified signal gets to the high level input, it goes into the sub's own amplifier, which at its front end has an active stage presenting a very high input impedance (i.e., essentially no load) to whatever is driving it. The high input impedance means that negligible current is drawn by the sub from the external power amp -- the sub's power amp is responding to the voltage going into it, but doesn't require significant current or power. It's just like a line level input going into a preamp or power amp, except that the voltage levels are higher.
The main speakers provide the proper 8 ohm loading to the external amplifier, and the sub's driver provides the 4 ohm loading to the OUTPUT of its internal amplifier, and everything's cool!
What should NOT be done, however, would be to at any time have the external power amp connected to the sub without the main speakers also being connected. Some amps can be damaged, or have their long-term reliability degraded, if they are operated without a speaker load.
Regards,
-- Al