Jive actually uses Salesforce.com (SFDC) for their back-end case management - what you see in Jive's support site is a custom integration between the two that utilizes the Jive discussion framework to track the support case history. I'm sure Jive's professional services team would be happy to chat with you if you're interested in that solution. ;-) We actually just finished working with Jive PS folks to roll out our own integration with SFDC case management that's independent of discussions.
In short, no case management functionality ootb, but you may find it very valuable to extend the Jive platform to also fulfill the roll of "support portal" for your customers. We did, and Jive certainly did as well.
Thanks Scott. I would assume therefore that with some work, I could do the same with Jira. That is quite interesting.