Though I’d hope that most legit hosts (ones that cater to personal projects, anyway) would “freeze” your account, and allow you to reactivate it once you have paid up to date.
Another thing, and one that I hope the Discourse team considers when they move toward providing hosting solutions, is the case of someone who has started a discourse-powered forum using the paid hosting solutions, who later wants to move to self hosting. (for whatever reason) Hopefully, there will be a reasonably easy migration path to move to a new server.