Decommissioning on-premises Exchange
The subject of decommissioning on-premises Exchange is most applicable to organizations that have created an Exchange hybrid environment. It might seem logical to consider decommissioning all on-premises Exchange after all mailboxes and email workloads have been migrated. However, it is important to note that if your organization wants to manage Exchange Online with the EMC, a minimum of one Exchange on-premises CAS must still exist in the forest.
If directory synchronization is implemented, Active Directory is then the source of authority, and Microsoft recommends not removing the last Exchange 2010 on-premises server. By removing the last on-premises Exchange server, you will be unable to make changes to the mailbox objects in Exchange Online because the source of authority is defined as on-premises.
The bottom line is that you should keep one Exchange 2010 CAS on-premises, for now. A more detailed discussion about this topic is covered by the Microsoft Exchange team on their team blog referenced in the following Inside Out sidebar.