In the case of RabbitMQ, it starts paging messages to disk, IIRC. If you run into descriptor / memory / disk limits, it starts turning away new messages until

In the case of RabbitMQ, it starts paging messages to disk, IIRC. If you run into descriptor / memory / disk limits, it starts turning away new messages until it returns back to a safe threshold. There's a certain amount it can do, but ultimately, you have to apply backpressure at some point unless you're willing to start losing messages at the message broker layer. After that, there's still a lot you could do: spool them to disk on the publisher, retry later, etc. You still risk message loss, filling up THOSE disks, etc... but again, something has to eventually give.