"What happens when a member doesn’t pay?"
It depends on what settings you have enabled in Stripe. By default, Stripe will mark the invoice as unpaid which revokes access in Memberstack. Scroll to the bottom for other options.
If a member doesn't pay, their payment fails, or they don't renew a free trial, they will lose access to the site. The next time they log in, they'll see a pop-up asking them to update or add a card to continue.
Manage failed payments - View in Stripe
You also have the option to automatically cancel a membership when their subscription goes unpaid. Select "cancel the subscription" if you need to revoke access in a 3rd party system.