I'm not sure which company you're talking about. I'll assume HP because what you're describing isn't a thing. However, HP has a lawsuit going on in the UK over practices similar to what you're describing. They can essentially disable your printer if you're subscribed to their instant ink program. The moment you terminate the service, your printer is a brick remotely, courtesy of HP. Even with the ink still inside the printer waiting to be used.
That's why it's important to research printers before making a purchase. Finding ones that have great third-party support is a good sign. Ones with continuous ink supply systems [CISS] available or chip cartridge resetters are best. Our line of Epson and Canon printers have that ability so you're not bending over to them buying ink.
Per drop, printer ink is worth more than Dom PĂ©rignon. Get the upper hand on ink for once and be done with paying ridiculous prices from the manufacturers.