A while back (June 2011), I wrote a post on how to implement TMG, Single Sign-On (SSO) and strong authentication with Office 365. It was, as it turns out, an incomplete story.
Tristan Watkins has written an excellent article on how to implement single sign-out using TMG with Office 365 and ADFS 2.0. It goes into great detail about issues with sign-out from non-federated proxies with ADFS/O365 and explains the various nuances associated with Office 365 sign-in…. you can read this article here: