Fill the cartridge with very hot solvent. Distilled water and alcohol for the 51626A, Cartridge Flush for the 51629A. Sit the cartridge in a dish of solvent overnight. Dried out Internal Sponge Inject 15 ml of pure ethanol into the cartridge. Then withdraw as much as possible. The ethanol will evaporate very quickly so you might not get much back out.
Re-ink the cartridge normally.
Burned Out Cartridges Many cartridges with internal print heads use electrical resistors to control the current to each nozzle. The ink actually acts as a cooling agent to keep the resistors from burning up. If the cartridge goes empty and printing continues, overheating occurs. If left too long this can burn out the cartridge. Each time this overheating occurs the life of the cartridge is shortened.