How come there is a sunbeam on the Pale Blue Dot-picture?

It isn't actually a 'sunbeam'. Rather, it's a band of dust associated with the Earth's orbit, that gets illuminated by the Sun. Because the camera exposure had to be highly sensitive in order to resolve the Earth at that distance, the dim light reflecting off this dust also shows up on the photograph. Comets also leave behind similar dust trails, which is what causes annual meteor showers.