It's a double-sided software issue.
First, the BIOS in your host computer needs to shut off the USB port or put the bus into "suspend mode".
Not all BIOS:es, even with the latest updates, can do either. Some are able to shut off USB ports, others will put devices into "suspend mode" and others will keep the USB buses alive.
In some, you have to find just the right option. Maybe there is some option for "awake from keyboard" or something, that you have to switch off, combined with "power saving mode". It is different from BIOS to BIOS.
Second, the firmware in the keyboard needs to make itself go into "suspend mode".
It is supposed to be mandatory for a USB device to auto-detect when the host puts the bus in suspend mode and then put itself in a low-power mode... but PJRC's USB source code (that most firmwares use) does not support it.
Some firmwares have suspend-mode support added in, however.
Then that firmware will have to be able to shut off the backlighting with an electronic circuit -- the host will not stop delivering power.
The common method for backlighting is not to drive LEDs directly but to use a LED matrix (connected similarly to a keyboard matrix) where the LEDs actually flicker at a rate higher than what the human eye can detect. Dedicated LED matrix driver chips tend to flicker at a fixed rate but alter the duration of each pulse (Pulse Width Modulation) to change brightness. With PWM you shuld have more range at the lower end than with direct drive, as with direct drive the lowest brightness would be limited by the LED's starting voltage.