To try and put it simply, the closer your voltage drops to the LED's threshold voltage (going downward from its rated operating voltage), the lower the current becomes, until almost no current at all flows and no more light is produced.
So in your little Pelican, as the battery voltage decreased, so did the current demands of the LED.
Eventually, the voltage on the LED will sag very close to the LED's threshold (somewhere around 2.4 to 2.8 volts for white), and current will be measureable in microamps, not milliamps. And at current that low, even dead batteries can chug along for quite a long time. Even little half-dead button cells will run for a long time with only 1-4mA on them, and most modern LEDs can produce usable light even at that low power. And it will take progressibly longer to dim out as the current demand of the LED continues to decrease.
That's why your Pelican was still usable.
But since most of the battery chemistry was used during the brighest several hours, there won't be very much left to run the LED even at a few mA, so another night will probably do it in.
Now, if there had been an incandescent bulb on there, the current will actually increase as the voltage drops and the filament cools.
In some cases, you can actually watch the flashlight go from dull yellow to dull orange to cherry red and finally to black extinction in a matter of minutes or even seconds because the bulb continues to draw more and more current, eventually exceeding the remaining capacity of the batteries and sucking what's left of them away quite rapidly.
Even at 0.1 volts or some other rediculously low value, the bulb will continue to draw current - as much as the nearly dead battery can generate. That's why you can sometimes find "stone cold dead" batteries in an incandescent flashlight that was left on, but in an LED flashlight that was left on until it went out, some voltage can still be measured - at least until the remaining good chemicals in the battery become neutralised or react with one another in storage (the self-discharge thing we all know and love).