Can Mqtt broker forward messages which have not been sent to any client ?
If a client has been connected and subscribed to a topic (at QOS 1 or 2) then disconnects the broker will queue messages to that topic until the client reconnects (as long as it sets the cleanSession flag to false when it reconnects) and uses the a fixed clientID
There is also the concept of retained messages. This is a flag that can be set on a message when published that means that the broker will remember the last message (retained) on a given topic and deliver this message to any client that subscribes to that topic before any other messages. It is just one message, not any other history.