What happens to messages that are not selected for delivery to the consumer by its message selector? This depends on the message model used.

For the publish-and-subscribe model, the messages are not delivered to that consumer; they are, however, delivered to other pub/sub consumers. This is true for both nondurable and durable subscriptions.

For the p2p model, any messages that are not selected by the consumer are not visible to that consumer. They are, however, visible to other p2p consumers.