Is there a way to make Runnable’s run() throw an exception?

You can use a Callable instead, submitting it to an ExecutorService and waiting for result with FutureTask.isDone() returned by the ExecutorService.submit().

When isDone() returns true you call FutureTask.get(). Now, if your Callable has thrown an Exception then FutureTask.get() wiill throw an Exception too and the original Exception you will be able to access using Exception.getCause().