Most cartridges these days have chips that keep track of how much ink they've ever released, and they refuse to work once that amount reaches the amount of ink they were shipped with.

I think that these chips are way simpler than that and only estimate the remaining ink based on the number of pages they have printed.

Sure, the details may vary. But the point is that if you don't take care of the chip, the printer will still consider a refilled cartridge to be empty and so refuse to print.

HP ink cartridges have a partial vacuum in them. That means when you open them to try and refill them, air gets sucked in and they no longer work.

It's possible to fix by taking the side panel off and squeezing the flexible membrane on the inside to get the air back out again.