It is my understanding that WebSphere clusters can be configured such that requests from the same session always go to the same instance in the cluster.
I see the following article:
If this is true, what happens if the instance goes down while the session is still active. Is the user logged out and asked to start the session again or the session is transferred to another instance?
Clusters can be configured to replicate (share) their session data.
Frontend HTTP proxies (like IHS + the WAS plugin, or any manually confiured HTTP proxy) can be taught how to maintain affinity with a backend server. In the event the frontend server cannot maintain affinity, it will use its own logic to try another server in the cluster.
Whether or not that other server can continue with the session, and how up to date it is, is part of the configuration of the HTTP session component in WAS.