Definitely, a number of people have died as a result of claustrophobia not really because of the fear generated but because situation like panic attacks can lead to complicated health issues like heart attack, cardiac arrest. Some died because they did not get the needed treatment that would save them from the situation.
Many people used to think they can treat claustrophobia by avoiding those things that always trigger panic and intense fear in them, that action will only keep reinforcing it. You would see them running away from elevator, they might decide not to use airplane when traveling all because of their fear of enclosed spaces.
Claustrophobia is an anxiety disorder which usually results to an irrational and intense fear of enclosed or confined spaces. One thing that kills those that are claustrophobic is what the generated fear can lead to, when they are extremely panicking because they find themselves in a very tight place, extreme fear can lead to panic attacks, though panic attack itself might not lead to death but it can lead to complications that might lead to death.