What happens if your service line comes off while driving?

Assuming you're referring to the trailer service air supply line in an air brake equipped combination, initially, nothing - you won't have trailer brakes and you'll notice a rapid loss of air pressure in the primary system when you apply the brake pedal (if you use the Johnson bar, you'll notice a rapid loss of pressure in the secondary air system). The service (blue) line only has air going through it when the brake valve or Johnson bar is applied - it's the emergency (red) line which is continually charged to keep the spring brakes released.