If node crashes and at that point of time messages are queued up in mailbox then how will those messages be reprocessed? If they can not be reprocessed then how can we say akka programming model is fault tolerant. This is the most basic use case for which we have to use persistent queues right now.
The messages won't be processed and will be lost; Akka does not guarantee message delivery - this is explicitly stated in the beginning of its documentation. However, this does not preclude one to make the program fault-tolerant. One of the simplest ways to do so would be to implement messages with acknowledgements and make actors re-send messages which were not acknowledged.