Definitely, claustrophobia can result to death. Claustrophobia is an anxiety disorder which usually results to an uncontrollable, persistent or irrational fear of tight or enclosed places. Phobia of anything generally results to anxiety and anxiety is a kind of mental apprehension or uneasiness.
What will show you have phobia for certain objects or situations is the irrational fear generated. A person who is claustrophobic will prefer making use of the stairs in a building that has elevator. He will never accept any suggestion to travel through the subway, all because he does not want to get trapped in a small place.
Claustrophobia can lead to death when the fear generated is becoming excessive because it has been medically proved that extreme fear can kill. So while you get scared of an enclosed space, you are increasing your chances of having heart attack and this might be dangerous and consequently lead to death.