I would imagine that during a sunset, for a brief moment of time, there would be a shadow of the earth seen in the clouds but I have never seen this. Why does it not happen?
To have a sharp shadow, you need a point source of light. But the Sun is extended enough that it does not set all at once, so there is not a sharp shadow. Also, there is refraction of the redder light, so instead of seeing a shadow, you'd see reddish clouds-- which I wager you see quite often (though much of that effect is from the way the atmosphere scatters away the blue light-- those effects are hard to disentangle but you know refraction matters because you see how the Sun's shape is distorted upon setting).