Poison message blocks single partition

An invoicing Kafka consumer (16 partitions, 8 instances, keyed by tenant_id) stops making progress for one tenant's invoices at 13:05 while every other tenant is fine. Dashboards: records-lag for partition 11 climbs linearly; partitions 0–10 and 12–15 are flat at ~0. The instance owning partition 11 logs the same business-rule exception, IllegalStateException: invoice already finalized, on the same offset, thousands of times; the handler catches it, logs, does NOT advance the offset, and retries the same record on the next poll. CPU on that one instance is moderate. How do you triage and mitigate?