How do exceptions propagate through a chain, and what do exceptionally, handle and whenComplete do?

A stage that throws completes exceptionally, and every downstream thenApply is skipped, carrying the failure along wrapped in a CompletionException.

• exceptionally(fn) runs only on failure and substitutes a fallback value.
• handle((value, error) -> ...) runs either way and produces a new value, so it can convert a failure into a result or the reverse.
• whenComplete((value, error) -> ...) runs either way for a side effect and leaves the result alone, which makes it the right place for logging and cleanup.

The wrapping catches people out: get() throws ExecutionException, join() throws CompletionException, and the cause is your original exception in both cases. And a chain nobody ever joins, gets or handles swallows its failure completely.