Turning on an LED based on light and darkness?
Saturation doesn't mean the collector current goes to zero. It means whatever is supplying current to the collector can't provide enough current to keep the transistor forward-active. (Also think about this: if collector voltage is 0, then voltage across R1 and D1 is 5 V, so there must be current flowing through those parts. Where else can it go but through the BJT then?)

When the BJT is in saturation, it doesn't (as far as back-of-the-envelope calculation models are concerned) control the collector current any more. Whatever is biasing the collector (Vdd, R1, and D1 in this case) controls the collector current.