I've never seen true unlimited chips on a Mimaki that didn't have some sort of chip writer built in. Usually you have to push a button or send a command from a piece of software to reset them. That's not to say they don't exist but I have yet to encounter them. I don't sell that kind of system but I have installed one from Triangle inks that had re-writable chips and a re-setter that would work semi-permanently. The re-setter would only have a set amount of recharges and would need to be refreshed by Triangle eventually. So it uses some sort of serial number system that the machine remembers is my guess.
If you look on your ink chip, on other side you should see small microchip. Usually it eeprom. What kind of eeprom is it? There are 2 known types one of the DS2430 and another DS2431. There are some devices which can rewrite this eeproms: