Plague typically kills by lung or heart infection. Gangrene is a common symptom but is not usually the cause of death; the lung or heart infection will kill you before the gangrene can. Left untreated, plague has a > 90% mortality rate. Even with treatment, it can still kill with great likelihood.
Infection itself is very likely as plague is highly contageous, spread through airborne means. Symptoms may take a week to display, so an infected individual could spread the disease to crowds of people before they even realize their infection.
