I commented above about this, it actually happened to my car. The pump overheated.
There were some natural gas kits sold that would not disable the fuel pump when you switched to gas. Some owners, when running out of gasoline, would switch to the gas. The fuel pump would keep running dry and melt. Something like this: http://2.bp.blogspot.com/_WafeVL7IZss/S5VP0fVNvuI/AAAAAAAAJP...
I believe the problem (or at least one of them) with early fuel injection was that the injectors would overheat if they didn't have have the fuel passing through them to cool the solenoid. Newer cars won't even attempt to fire the injector if a high enough fuel pressure isn't sensed.
