So yeah, the engine will die after a while.
But look at it this way. A 40 or 46 size engine in a trainer, which usually has an 8 ounce tank, will fly for nearly 10 minutes at wide open throttle. (A 40FP when using throttle, will run about 20 minutes on an 8 oz tank.)
10 minutes is a long flight (national average according to a survey is 6 minutes). So, you'd have to be pushing the limits of flight time for your tank to be that empty, and not many people are going to climb high enough (at the end of a long flight when you know fuel's getting low), to be able to dive far enough to starve the engine. :stupid:
Whew! That being said, don't worry about it!
Dennis-