Receiving emails and newsletters is different than receiving autoresponders.
They have separate subscriptions. In order for inactive clients to not receive emails and newsletters anymore, indeed, they need to be unsubscribed from emails, respectively newsletters. In order not to receive autoresponders, they need to be unsubscribed from each autoresponder they are currently subscribed to.
All of this is done in their Personal Info page (CLIENTS TAB > CLIENT NAME > PERSONAL INFO > Subscription Settings section/Autoresponders section respectively).
After a long debate between various requirements from coaches, it was established that, as long as they are subscribed to emails and autoresponders, inactive clients will continue to receive them because a majority of coaches want to stay in touch with their inactive clients.
Only DELETED clients no longer receive anything for obvious reasons.