This is what disputing charges is for. Once you have told them, even once, that you are canceling your subscription, any further charges are fraud and you should respond accordingly.
I agree with this, provided that you did notify them in a reasonable way.
A random email from an unverified address to the first point of contact you can find with Google is not a reasonable way, for the purposes of this discussion. Nor is a casual ambiguous statement during a long phone call whose meaning clearly wasn't understood, if you don't clarify it at the time but then quote it out of context later.
Personally, I like the rule of thumb that it should be no harder to cancel a subscription than to take one out and you should be able to give that notice via the same channel(s) you could use to sign up in the first place, but no-one on either side is required to go any further than that. It keeps everyone honest, but it's also obviously reasonable and proportionate.
I wouldn't consider the second example telling them, and I wouldn't consider the first you, but I can see how it might be interpreted that way, so fair point.
Ultimately, though, they're periodically asking you for money; if you decide to stop giving them money, then things need to work out such they don't get any more of your money.
Ultimately, though, they're periodically asking you for money; if you decide to stop giving them money, then things need to work out such they don't get any more of your money.
Agreed, that is the important thing (though it implicitly assumes that you don't have some contractual obligation to continue making payments for whatever reason).
I'm not in any way advocating making legitimate cancellation artificially difficult here. I dislike shady businesses that do that as much as anyone else. I'm just also seeing it from the other side, as someone who has run subscription-based services, because sometimes customers will give ambiguous or conflicting signals and then assume you magically know how to interpret them correctly.
A particularly common one in my experience is a subscriber sending an email to ask how to cancel, receiving a prompt reply from you answering their question, but then not actually doing it. Contractually speaking, there seems to be no doubt at that point that their subscription continues and further charges are legitimate. However, if they just forgot to act on the response, and then they come back six months later claiming that they're still being charged after "they asked to cancel", that's always an awkward situation. It gets more awkward if they really haven't been using your product/service since that time, or if they haven't actively been using it but they do have some sort of data stored in it that would be deleted if their subscription ended. It can get much more awkward if they really did literally ask to cancel, but in an insecure/unverifiable way such as an ad-hoc email, and if you did reply advising them of that and explaining the correct procedure, which they didn't then follow.
Within reason, we tend to refund as a good will gesture in this sort of situation as long as we believe it was an honest mistake by a customer, but I don't think either the law or whatever payment service was used should be imposing any sort of obligation in that case. Insisting on a clearly defined cancellation process does have the advantage of being unambiguous and therefore reducing the risk of that sort of confusion.
This is what disputing charges is for. Once you have told them, even once, that you are canceling your subscription, any further charges are fraud and you should respond accordingly.