Shutting down a dedicated server seems to result in the expected behavior, where both messages are received, but it may be possible for the circumstances causing the issue to occur on a dedicated server as well.
Reversing the order in which UNetDriver::Shutdown sends these bunches will result in only the NMT_Failure message being received on the client.
Create a listen server and a client instance.
Shutdown the listen server instance.
Expected: The client will receive both a ENetCloseResult::HostClosedConnection close reason message, as well as a NMT_Failure message with a "Host closed the connection" error.
Actual: The client only receives the close reason, so the only network error that is broadcast is the "ConnectionLost" failure from UWorld::TickNetClient.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-206039 in the post.