Chargebee's dunning sequence ending with no successful payment is really just a signal. What should happen next, pause the account's access immediately, give it a short grace period first, flag it for a success rep to call before anything gets cut off, is a business decision Chargebee doesn't make for you, and by default nothing downstream necessarily knows that decision needs making at all.
The account's status after dunning exhausts also needs to show up correctly wherever else it matters: in a CRM a sales or success rep is looking at, and in the product's own access controls. Those don't automatically agree with Chargebee's record unless something keeps them in sync.