Why does water remain in the bottom chamber after brewing with a moka pot?

This is deliberate.

In a moka pot, the downward spout of the funnel does not reach all the way to the bottom of the pot. Brewing will stop once the level of water in the pot falls below the bottom of the funnel (if you carry on brewing after this point, you'll be making coffee with the superheated steam, which will be burnt and bitter).

I'm not sure why this is how it works, but I guess it's to prevent the pot from boiling dry, and retaining a thermal mass in the bottom pot to help it cool down again.

Original image from Wikipedia article on moka pot, thanks to user Alborzagros!