Messages that exceed their redelivery count will be moved to dead letter queue.
If this move of messages to DLQ happens concurrently, it will raise

16:38:19,233 | WARN  | 99.1:55704@61616 | JDBCPersistenceAdapter  | 219 - org.apache.activemq.activemq-osgi - 5.11.0.redhat-630224 | 
JDBC Failure: org.apache.commons.dbcp.PoolablePreparedStatement with address: "..." is closed.

Full stack trace in comment below.
The broker typically shuts down as a result of this exception.