Short answer - nothing different than if there was a subscriber on that channel. Publish (senders) and subscribe (listeners/receivers) are completely decoupled so there is no dependency between the two.
All published messages are cached for quick retrieval when a subscriber returns from a network disconnect. In other words, if the client is configured for message catchup, those missed messages can be recovered when the client comes back online an resubscribes to the channel.
Message are cached for up to five minutes and limited to the last 100 messages. If Storage is enabled for the key set (pub/sub keys), then all messages are stored for as long as that retention is configured for Storage. This allows a client application to get messages (using the history API) that were sent while that client was offline for a long period of time.