Out of fuel between exits: how petrol delivery actually works
Two mechanical notes worth knowing. First, on a modern petrol car the fuel pump sits inside the tank and is cooled and lubricated by the fuel around it, so repeatedly running the tank to the last litre in summer shortens the pump's life; treat a quarter tank as empty from June to September. Second, after a true run-dry, the car may need several cranking cycles to re-prime, and some diesels will not self-prime at all, in which case the fuel delivery becomes a fuel delivery plus a technician. Say what the car is when you book so the vendor arrives prepared.
While you wait, the E311 shoulder rules above apply in full. An out-of-fuel car is legally and practically identical to a broken-down one, and a stationary car in the shade-free middle of the afternoon heats up fast. Take the water, take the children, and wait behind the barrier, not in the car with the windows up and no AC.