Intuitively I would say it continues down to zero almost linearly. I would guess the graph doesn't go lower simply because it is outside the scope of normal usage, just like car fuel usage is specified at average driving speed rather than at a snails pace.
I have LED lighting at home with LEDs rated at 700mA (although I run then at 500mA) but overnight I dim them by limiting the current to 1mA, they give just enough brightness to see by.
If you need more accurate control at very low brightness, I would suggest PWM dimming would be more predictable.
Brian.