Is it possible to die from Bed Bug bites?

Yes.

While rare, some people may be so allergic to the bites that they suffer from anaphylaxis which is life-threatening. It would be highly unlikely but as with any allergic reaction there are extreme cases which result in death. The odds of death from blood loss are limited but people who have rather severe cases may suffer from anemia, which may also be life threatening, but you would have to have a severe case of bed bugs in order to have this level of blood loss and in most cases anemia is not going to be deadly. With that said, allergens and loss of health all impact overall well-being which can make someone more susceptible for other illnesses including the more severe. Prior to finding out the cause, I was diagnosed with appendicitis about halfway through our infestation. I had a severe rash on my right side. As it turns out, it was most likely mesenteric lymphadenitis, swelling of the lymph nodes in the abdomen, and the fact that it was on the right side was because there was a rather large number of bites all over this side of my body. But to answer your question, it is highly unlikely that one would die from a bed bug infestation and more likely the irritation would become so unbearable that the little buggers would be found beforehand.