Hi Sara - good topic. I agree with your comments that a member's content, profile, points, etc. should be able to stay with her and move with her. However, the exception comes when the profile and content is also associated with Support cases. For CRM systems where your access is 'all or nothing' then I believe you would have to retire the profiles associated with the previous companies and start a new one. This is true for the CRM system at ArcSight (we use RightNow). If a person leaves Company A, he should not be able to log Support cases for that company anymore. If he goes to work for Company B, he gets a new Support CRM profile under Company B.
In the Jive community, the Support cases are handled by Secret Groups. I would think that the Jive Support team (or your previous companies) would just remove you from the secret Support groups for those companies. You would no longer be able to open or view Support cases for those companies. Your content in the public areas of the Jive community should remain. And, on your profile, you're able to edit your email address and company name, so you are no longer linked to the previous companies on your profile.
For the ArcSight customer community that we run on Jive, I sometimes see a member open a new account when he changes jobs. For these cases that I catch, I reach out to the member and ask if he just wants to update his existing profile, so that all of his history, content, join date, etc. remain with him, rather than starting over.
Sara, if you were talking with a Jive Support person, I would recommend double checking on the options? I think Deirdre Walsh's account is a great example. She joined the Jive Community in 2007 as a customer and now she is a Jive employee. If you look at her profile, the join date is still 2007 and her content as a customer is still there.
Hope this is helpful! And congratulations on your new job!