The S1 UE context is being deleted, as to bearers - for GBR bearers MME initiates Dedicated Bearer Deactivation procedure, - for non-GBR bearers MME starts the preservation and suspension by sending Suspend Notification message
The CSFB procedure is covered here http://www.lteandbeyond.com/2013/09/CSFB-Mobile-Terminating-Call-in-Active-mode.html
What happens for an UE at MME, which gets triggered "UE Context Modifcation Procedure" for "CS fall back" ?