In the pub/sub model all messages which are published to an address will go into any applicable subscriptions. If no subscription exists then the message will simply be deleted. There are two types of subscriptions - durable and non-durable. A durable subscription, once created, will remain on the broker and receive messages whether or not the client is connected. A non-durable subscription only exists while the client is connected.
If your client creates a durable subscription then it will be able to fetch any messages that were sent while it was disconnected, but obviously any messages published before the subscription is created will not be available to that client.