HP's position on the printer not operating with an empty cartridge is based on a premise that the printer could be damaged otherwise. If you print with black ink only, the other ink cartridges must have ink for the printer to print. If one or more color ink cartridges are low but not empty and you want to minimize the use of color ink, change the settings in the HP software to print with black ink only (grayscale). When an ink cartridge is depleted, you must replace it before you can print. This helps to prevent issues such as printhead clogs and poor print quality. Some ink from all the ink cartridges is used in periodic servicing tasks.

Your printer is designed to print only when all ink cartridges have ink. The printers listed in this document cannot print when one ink cartridge is empty.

Per the HP Customer Support Knowledge base (excerpts): If any color cartridges are low, you can set it on black-only to minimize the use of color, but the color cartridges cannot register as empty. The Officejet 8710 is among the HP printers that cannot print if any ink cartridge is empty (there is no override provision as some printers have).

How to make my printer print black only