Most stereos have two power connections - switched and unswitched. Switched power runs the unit and unswitched power is a trickle for the clock and station memory. The Becker is able to run off unswitched power as well.
It's a simple matter to wire your Kenwood to work with the key in or out. It's a much more complex matter to have the radio turn off then you turn the engine off and be able to turn on the radio again with the key out.