Core answer
Start here. This is the direct spoken answer to practice first.
Why this question matters
A broker is an infrastructure dependency and a finite buffer. Publisher outage, consumer backlog, and downstream saturation need explicit admission, durability, degradation, and recovery policies.
I would first separate publisher outage from consumer backlog. If the broker is unavailable when the API needs to publish, the API can fail the request, store work locally in an outbox for later dispatch, or run in a degraded mode depending on the business action. If consumers are behind, producers may still publish, but user-visible work may be delayed. The system needs to communicate the right status.