Are sites taken offline when payments fail / subscriptions lapse?

What happens to a pro site when a payment fails? Is the site taken offline?

Background: Given that I'm aiming for strong relationships with my clients on a network I'm planning, I think, ideally, I'd like sites to be left online for discretionary removal. I'd be OK with publishers not being able to add to or edit their sites when there's no active subscription, but I'd want to be quite lenient to clients (most of whom will be community/charity groups) around failed payments...