Every gym membership I’ve had would let you finish the current month.

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

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

I'd consider that more analogous to what HP did if they made you send back all of your old cartridges, but they don't. HP doesn't treat the cartridges like you're renting them, and doesn't care about getting them back, just that you can't use them anymore.

The gym is selling access to the equipment and HP is selling access to the printer. Both the keycard and the ink cartridge are tools provided to allow you to use your access. Neither require you to return the tool providing you access after you cancel.

Analogies keep failing