Both webhooks and looking at your subscription settings are important. Here's some documentation on how to do both.

https://stripe.com/docs/webhooks

https://stripe.com/docs/subscriptions/lifecycle

The webhooks are important because stripe doesn't email you about failed payments you need to do that on your own.

And the default for a 3 time failed subscription over a 15 day period is to remove the subscription which you can easily change to keeping it but labeling it unpaid among other things.