Yes, as @Landowski says, you’ll need to set up a webhook to listen for the “subscription canceled” (or whatever it’s called) event. Stripe has pretty good documentation.
Webhooks are just automated http requests sent from one server to another (from Stripe to your Bubble app in this case) which are triggered when certain events occur; so your Bubble API endpoint functions as a “listener” for Stripe’s webhook events.
One way to initialize your endpoint is to click the “Detect data” button and then temporarily change the Stripe webhook to include the “initialize” path parameter in its request URL (done via the Strip dashboard), and then cancel a subscription in your app to actually trigger the event so that your endpoint can capture the webhook data (which will have information about the customer and subscription status). And don’t forget to remove the “initialize” portion of the webhook URL once initialized.
Anyway, that’s the gist of it.