As dzug2 points out, the printers only calculate that the ink should be running out soon and the printer will keep on working as long as there is ink in the cartridge,
For anyone that's interested, I've always refilled my cartridges for the last ten years, and on my last printer (before it died electrically!) I refilled the same black cartridge for 30 months. The trick is to refill well BEFORE the cartridge runs dry.
My new printer now uses chipped cartridges but I still refill them. The printer still tells me that they should be empty but by knowing the weight of a full cartridge and an empty cartridge, I check the cartridge weights regularly and refill as and when necessary.
The so called "half empty" cartridges supplied with the new printer have also been refilled and are still in use.