i would guess that's a problem inside the wiper motor. when switch power is turned off, the motor is supposed to keep supplying power until the arms go all the way down (park). this is the way it worked in older cars, i guess it could be controlled by a relay, but i'm not aware of any relay for this purpose.
i'd start my checking the electrical connector at the wiper motor. one wire should have power as long as the key is on.