ExecutorService that rethrows exceptions

I need to execute a task using any Executor or ExecutorService. The task (Callable or Runnable) is supposed to run infinitely, but in case of any exception it should be rethrown to the thread that submitted the task.

I know that future.get() would throw ExecutionException for me:

  ExecutorService executor = Executors.newSingleThreadExecutor();
  Future<?> future = executor.submit(new Task());
  future.get();

However, in sunny day scenario I block on future.get() indefinitely, so I cannot use it.

Is it possible to have any Executor that simply throws exception when underlying task fails?

I don't think it is possible to do this with simply using Executors.
You can consider using a try-catch block in your Task and add the exception on to a queue in the catch block.

try{
   //perform task
  }catch(Exception e){
     queue.offer(e)
  }

Create a thread that reads the exception from the queue.

public void run() {
        Exception e;
            try {
                    e = q.take();
                    e.printStackTrace();
            } catch (InterruptedException e1) {
                    // TODO Auto-generated catch block
            }
    }