The kick-down cable is part of the transmission, which is tied to the accelerator. When a person releases the gas pedal, the kick-down cable moves the valve inside the transmission to transition to a lower gear when the vehicle decelerates.
The kick-down cable has a similar function as that of a fuel injector; when decelerating, the cable downshifts the transmission, just as the fuel injector supplies less fuel. The kick-down cable monitors the position of the gas pedal and adjusts accordingly.
Newer cars are computerized, and the computer monitors the down-shift activity in order to protect the engine. Computers are able to detect problems much sooner and warn the driver earlier in the process.