Follow on...

My examples failed because I didn't properly think them through, and
consequently did not account for pitch. Here is what I should have written,
with my corrections in all caps...

You take an airplane to 1,000 ft AGL, and trim it so it is flying perfectly
straight and level. You then close the throttle slightly, resulting in a
slight descent. IF PITCH TRIM IS NOT CHANGED, eventually you will impact the
earth, even though the airplane as a whole (and probably all of it's
component parts) are still "flying".

You then take an airplane to 1,000 ft AGL, and trim it so it is flying
perfectly straight and level, but this time you completely close the
throttle WHILE ATTEMPTING TO MAINTAIN THE ORIGINAL PITCH. In a short time,
the wings will stop producing enough lift to keep the airplane in flight, it
will pitch down and impact the earth, even though some of the airplane's
component parts may still be flying.

I believe these scenarios are correct, and I promise to do better next time!
g