Most sites will just automatically cancel your subscription if your card fails without an explicit cancel. But the real slimebag ones will keep it going and sell the debt to a collection agency.
Can you take someone to small claims court for claiming you owe them money, in order to not pay?
I moved out of California on 7/10, and my vehicle registration expired on 7/14.
The Vehicle Registrations Collections office sent a “Demand for Payment” to my new address because my registration is past due. I have to call to contest.
How can they charge me money for something I never wanted or legally needed?
What's the alternative? Don't ever assume that any resident wants to renew, but silently start accruing fees and potential criminal charges that'll be levied when they inevitably realize they forgot to re-registry, and do so months late? Sure that may be technically legitimate - the onus is on the resident, after all - but it'll lead to a ton of unnecessarily pissed off people.
Assuming the call they want is simply to confirm that you have moved out of state, I think that's a reasonable ask.
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Aside: Wisconsin sends multiple reminders before registration is due. It can be via mail, or email. And there are late charges, but only $10 or so (applied by the DMV - driving without registration is also a criminal issue that police can enforce separately if you're driving on public roads).
I thought it was a pretty good system.