Since Soapbox Mailer is quite the versatile app, while some organizations may use it for newsletters that require unsubscribe functionalities, other organizations use it for ad-hoc emails. With this in mind, we've created Soapbox Mailer to be rather flexible in the way unsubscribes are recorded.
When an email recipient clicks the unsubscribe link you've included in your Soapbox Mailer email, their Campaign Member related to that email will have the checkbox field "Unsubscribe" marked with a check. Since our community has a number of different ways of then denoting subscriptions in their own Salesforce instances, this action does nothing more than check the box for this campaign. To automate any marking of unsubscribing to a particular list on the Contact record would require a simple trigger or Process Builder flow to be created by your organization in Salesforce to record it appropriately for your specific needs.
If you're looking for a subscription list management process, we'd recommend this subscription and list management best practice.