Will old sessions still bound to the old license server migrate to new license server upon loss of heartbeat?

We recently migrated our academic & classroom concurrent licenses from one server to another:

• all clients use 2 line SERVER cname ANY port / USE_SERVER license file so they never have to adjust anything
• server license files use real host name or own alias
• install license software on new server with new host name or alias
• deactivate licenses on old (license service remains up)
• activate license on new, download new codes, start new license service
• test new with a client configured to underlying host name or alias
• adjust DNS cname to new server
• all new sessions use new server
• all previously started sessions remain "bound" to the old server as it must cache the IP or such
• these gradually wither away as old sessions are ended
• request remaining old session users save & restart

Eventually though it is time to turn off the old server, or it may crash, or the old MLM license service may accidentally terminate. The old service cannot be restarted as it is no longer activated, ie it has been living on borrowed time.

What happens to any remaining "old" sessions once they detect loss of heartbeat? Will the IP or whatever be uncached on the client so it can "rebind" to the current SERVER cname and seamlessly carry on? Is there a way to force this? Or will the session be permanently "zombied"? Will any work still in progress be saved? Some users run jobs that take weeks to complete.