Does shaking a laser toner cartridge yield more toner?

My grandparents' Brother HL-3170CDW always underestimates the amount of toner remaining; they always manually override the “Toner Empty” message, and reset the toner cartridges to printer another 100-200 more pages.

As the toner cartridge will have been lying in the printer for months, does removing it and rocking the toner (to and fro) loosen the toner and unleash more of it?

Yes, on my HP Laserjet 1200 I always turn/shake the toner as soon as printing gets thin, and I get at least 30 pages more. After that I might be able to turn the cassette additional times, as soon as printing gets thin and repeat this until the cassette is really empty. That might be about five turns of shaking for me.

Yes, on every laser printer I've used, rocking and rotating (not shaking) the toner has yielded the ability to print more pages.

My technique is:

1. Turn off the printer.
2. Remove the toner cartridge.
3. Carefully carry it to be over a sink.
4. Hold it at each end.
5. Rock it side to side gently 5-6 times.
6. Rotate it 360 degrees in one direction (like you would roll a packing tube) 5-6 times.
7. Rotate it 360 degrees in the other direction 5-6 times.
8. Reinsert the toner cartridge.
9. Wash my hands.
10. Turn on the printer.

Has worked every time for many years!