As per the spec :
https://download.java.net/java/early_access/jdk25/docs/api/java.base/java/util/concurrent/ForkJoinPool.html#schedule(java.lang.Runnable,long,java.util.concurrent.TimeUnit)

RejectedExecutionException - if the pool is shutdown or submission encounters resource exhaustion.

A sample code below
===
try (final ForkJoinPool p = new ForkJoinPool(1)) {
            Runnable task = () -> {
            };
            p.shutdown();
            p.awaitTermination(2000, MILLISECONDS);
            assertTrue(p.isShutdown());
            Assert.assertThrows(() -> p.schedule(task, 2000, MILLISECONDS), RejectedExecutionException.class);
        }

===
expected to throw RejectedExecutionException,

Actual : java.lang.IllegalStateException

java.lang.IllegalStateException
at java.base/jdk.internal.vm.SharedThreadContainer.start(SharedThreadContainer.java:146)
at java.base/java.util.concurrent.ForkJoinPool.startDelayScheduler(ForkJoinPool.java:3468)
at java.base/java.util.concurrent.ForkJoinPool.scheduleDelayedTask(ForkJoinPool.java:3492)