Thread exhaustion (OutOfMemoryError) with CXF AutomaticWorkQueueImpl as main suspect

Issue

JVM is failing with an OutOfMemoryError due to thread exhaustion. After taking a thread dump, most threads appear to be stuck like this:

"default-workqueue-1" daemon prio=10 tid=0x00007f1049759800 nid=0x3a95 waiting on condition [0x00007f1054232000]
   java.lang.Thread.State: WAITING (parking)
    at sun.misc.Unsafe.park(Native Method)
    - parking to wait for  <0x0000000091180068> (a java.util.concurrent.locks.AbstractQueuedSynchronizer$ConditionObject)
    at java.util.concurrent.locks.LockSupport.park(LockSupport.java:186)
    at java.util.concurrent.locks.AbstractQueuedSynchronizer$ConditionObject.await(AbstractQueuedSynchronizer.java:2043)
    at java.util.concurrent.LinkedBlockingQueue.take(LinkedBlockingQueue.java:442)
    at java.util.concurrent.ThreadPoolExecutor.getTask(ThreadPoolExecutor.java:1068)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1130)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615)
    at org.apache.cxf.workqueue.AutomaticWorkQueueImpl$AWQThreadFactory$1.run(AutomaticWorkQueueImpl.java:353)
    at java.lang.Thread.run(Thread.java:724)

How to we solve this?