Hi Lynn, when we end support for iOS 10 and Android 6 on July 28, 2019, push and app-generated passcode authentications will continue to function on installed apps. We have no plans to terminate functionality for these features of the app on older OSes.
The end-of-support milestone simply means that our development and technical support engineering teams will no longer be able to help troubleshoot issues with the application on iOS 10, Android 6, or older.
However, if you would like to restrict which authentication methods can be used, I recommend considering an authentication methods policy. In addition, we will never automatically send a push to a user if they do not have Duo Mobile installed and activated. They may utilize other authentication methods, such as phone callback, instead of Duo Push.