The reason sinks have traps is to prevent sewer gas from getting into
your house. If the trap runs dry, you will get that sewer smell.
However, usually there is no trap on the vent pipe (shouldn't be one
anyway). So, if the vent pipe isn't vented to the outside, you will
get sewer gases inside. Extend the vent pipe at least to the attic
space, but, better yet, to the outside.