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One could, although it's not clear why one would want to. If anything, it's easier than a normal coaster brake, since all you have to do is use the reverse torque to actuate the brake. Any mechanical or hydraulic method would involve a fair amount of backlash, but you could eliminate that for all practical purposes (i.e. the actuation backlash would be less than the inherent backlash in a roller chain drive) by using a load cell to detect reverse torque and electrically actuated brakes.
Could one design a fixed rear wheel with a back-pedal brake?