DIAGNOSIS The printer's page counter has hit its limit, not an actual physical sensor. Brother cartridges for this model have a chip that estimates life based on page coverage, and it locks out printing when it thinks it's done.
FIX You can temporarily override this to squeeze out the remaining toner. With the printer on, open the front cover. Press and hold the 'Go' (the button with the half-circle icon) for about 10-15 seconds until all the LEDs light up. The message should clear and you'll get a few dozen more pages. This is the built-in override procedure.
IF THAT DIDN'T WORK The override only works if there's still a usable amount of toner in the cartridge. If it genuinely is empty or extremely low, the printer will refuse. Shake the cartridge gently side-to-side (cover the drum with paper to avoid dust) to redistribute the remaining powder, then try the 'Go' button procedure again.
HEADS UP The print quality will degrade as you use this override—pages will get lighter and you might see streaks. It's a stopgap, not a permanent fix. Eventually you'll need a new TN-660 cartridge.