when i ran out in my '08, it kept going on electric with no trouble lights. i didn't even realize until the battery got low. then it shut down and the whole board lit up. i assume that the pump shut off with the engine, but probably ran until all the fuel was out of the injectors
All I know is that any time I ran out of fuel in the last 30 years or so, the engine always started immediately after I put fuel in.