Your phone requires a certain amount of wattage to run, which is a combination of voltage and current.
V *A = W
As your battery drains, the voltage will drop but the phone still needs the same amount of wattage to keep running. That means the current draw has to rise to offset it. It also means now the battery will be drained quicker. At very low percentages, there is barely anything left in the battery, but the phone is still trying to run full steam ahead, and the battery simply can't keep up.
As a side note, it's not a good idea to habitually run the battery down that low. Doing so will cause excess wear on it, leading to a premature loss of capacity. Ideally you should try to keep it between 40-80% to maximize overall life.