Actor Mailbox after crashing/restarting

If an actor is in the middle of processing a message and it throws an exception, but it is supervised with the restart strategy do all the queued messages in the mailbox get carried over? Does the message it crashed on get carried over? If not for either of these questions how can I make it so that they do? Thanks!

On a supervised restart the rest of the mailbox is kept and the actor instance is restarted to continue processing the next message.

The message crashing the actor will quite likely crash it again, so retrying processing of that after restart is generally a bad idea as it could end up with the actor getting stuck in a crash-retry loop.