My opinion is if your engine was tuned
correctly, it will not harm it running out of
fuel.
I have done this hundreds of times with no
damage even in a killer engine.
If just before running out of fuel the car
was tuned:
1) Tuned Slightly rich, it will speed up for
a brief moment just before it dies as you pass
through the "Ideal performance" mixture stage.
2) Tuned for ideal performance, it will fall
off in power just before it dies as it passes
through the too lean stage.
3) Tuned too lean to start with, it will bog
down noticeably and may blow the plug as it pass
though the "way to lean you just screwed up
stage". This can cause some damage to the piston
and sleeve if the element wire breaks and falls
in to the engine.
However, the brief lean moment should not
hurt the bearings, bushings, rod, crank etc. if
you are using high quality fuel.