Certain bacteria that produce hydrogen sulfide as a waste product would die if directly exposed to oxygen. The hydrogen sulfide reacts with oxygen, removing it and so preventing it from harming the bacteria. Furthermore, the hydrogen sulfide tends to kill other organisms in the area, thereby providing the bacteria with a source of food. As a result, a dense colony of these bacteria produces for itself an environment in which it can continue to thrive indefinitely.
The statement 'The bacteria can continue to thrive indefinitely only in an environment in which the hydrogen sulfide they produce has removed all oxygen and killed other organisms in the area' is most strongly supported by the information above.