To extend the strained analogy, they do let you finish the month (of printing pages). The complaint here is more “my keycard barcode is still legible, but it stopped working at the end of the month”.

    Cancellations and plan downgrades are effective after the last day of the current billing cycle.

https://www.hp.com/us-en/shop/cv/instantink

As does this one from HP. The OP mentions explicitly that they let their subscription expire, and the printer THEN stopped printing.