If a contact is on a private group and sends an unsubscribe request, they will receive a confirmation message with a link to re-subscribe. The re-subscribe email will be processed as a failure however since the group is not public.
Solutions that I can think of ranked in order of quality:
a) The full solution to have hash re-subscribes that work for both public and private groups. This is described here http://issues.civicrm.org/jira/browse/CRM-1799 but is not slated until 2.0.
b) Not process re-subscribe links in the unsubscribe replies for private groups.
c) Mention in the documentation or interface that the message templates for private groups should not contain re-subscribe links.