You sound a bit confused, so I'll just explain it in a way you might understand better.
When coasting downhill in gear with a modern EFI engine the engine is being "driven" by the road, which is turning the tires, which turns the driveshaft, transmission, and engine. The fuel demand is zero, no fuel is delivered, and the engine is putting out no power. The engine is actually "absorbing" power in the form of engine braking, which will slowly slow you down. In this state you are using no fuel because none is required. The engine doesn't die because it's not disconnected from the drivetrain or the road, all of the other systems are still functioning as well, there's just no fuel so the engine is acting like a big air pump.
When freewheeling downhill in neutral, the engine is disconnected from the road so in order to stay running in this state requires fuel, just as if you were sitting parked in your driveway. Take away the fuel here and the engine dies, you lose power steering, eventually you lose power brake assist, etc.
Maybe thinking about a bicycle will help?
Coasting downhill in gear is sort of like coasting downhill on a bike with your feet still in the pedals. Let's assume it's an older bike that can't freewheel, if the bike is moving then the pedals are moving. In this scenario your feet never leave the pedals, your legs are moving but you're not doing any work. Have you disconnected anything from the chain or tires by coasting? Nope. Are you able to transition to pedaling without changing anything else? Yup. Are you what's moving your legs? Nope, the movement of the wheels on the ground is moving them for you.
Now let's do the same scenario, only this time you take your feet off the pedals. If you want to move your legs now, what supplies the power/energy? Your body. Is it easy to transition back to pedaling now that your feet are removed from the pedals which continue to spin at a pretty fast rate? Nope.
Not the best example, but maybe it helps get the point across. Kinetic energy turns the engine and keeps it "running" when your foot is off the gas but it's still in gear. Kinetic energy requires no gasoline.