Why don't dry aged/hung sausages go bad?
It is due to a combination of several factor, depending on how the particular sausage was made:


Dry cured sausages contain curing salts, a mixture of regular salt and sodium nitrate (which breaks down into sodium nitrite), which prevents the growth of botulism while the sausage cures.
Meat for dry cures sausage is also often frozen to specific temperatures for prescribed periods of time to kill any trichinosis which may be present.
As the sausage cures, it becomes too dry and concentrated in salt to foster pathogens, as well as too acidic from the action of friendly bacteria, and thus is relatively shelf stable.  It may also simply have acid ingredients as part of the initial recipe.
Modern cured sausages may also be subjected to irradiation, cooking, or another "kill step" to satisfy the needs of regulatory agencies, according to the New York Times.


See also:


FSIS 
Food Safety News