How is it possible for some organisms to survive using only fermentation and not cellular respiration?

Both of these processes can happen thanks to alternative glucose breakdown pathways that occur when normal, oxygen-using (aerobic) cellular respiration is not possible—that is, when oxygen isn't around to act as an acceptor at the end of the electron transport chain. These fermentation pathways consist of glycolysis with some extra reactions tacked on at the end. In yeast, the extra reactions make alcohol, while in your muscles, they make lactic acid.