I've read of a technique with constant-current power supplies. (The power supply may be PWM controlled but the current through the LED is usually DC.)
The LED is simply "shorted out" to turn it off (with a MOSFET, etc.) and the constant-current power supply just happily continues to send the current through the short. But, you'd have to control the timing and I can't predict if the power supply would have a short-duration glitch when the voltage suddenly changes.
...The application I was reading about was just a visual "blinking" application with a power supply that wasn't designed to do that.