How does appendicitis lead to death?

Bad complication: Death from appendicitis is extremely rare in the modern era. With good surgical treatment and potent antibiotics, most patient recover just fine. However, if the diagnosis is delayed, patient suffers from significant systemic illness, allergic to the appropriate antibiotic, has resistant infection that lead to severe sepsis, death is an unfortunate complication.

Worsening infection: Appendicitis is an infection of the appendix. In neglected cases or in vulnerable populations (e.g. Elderly), the infection can become systemic (spread throughout the body). This can result in shock, organ failure and eventual death. Death from appendicitis is unusual but not unheard of.