Not used to my new Jazz, I ran my tank very low on its first long trip. Past ANY miles remaining and I think it took around 40 litres, if I remember correctly. No harm done (then) and not yet (4 years/39000 miles later). But time will tell as explained below:
Don't know how much this applies to the Jazz, however I know that many cars' in-tank fuel pumps (depending on design and positioning in the tank) rely on a certain level of petrol for cooling. Too low a level of fuel and parts of the pump are not sufficiently immersed and cooled; also, the pump ultimately begins to starve intermittently with 'fuel slop' when cornering/accelerating/braking/hills. Early on, the engine may not 'notice' it. Without enough cooling petrol, the pump heats up. This causes wear and tear on critical components and over time (p'raps thousands of miles later) premature, expensive pump failure results.
Not only that, there's always a chance of sucking up undesirable 'crap' and water (some is inevitable from atmospheric condensation on the inside walls of a part-empty tank) that would otherwise remain in the bottom of the tank.
And so I think it's good policy always to fill up not too long after the warning light comes on, if not a little sooner by keeping an eye on 'miles remaining' and the gauge needle.