Is it possible to die from chemotherapy?

YES. Chemotherapeutic agents can and do have significant toxicities and can lead to death. So (1) see a reallly good oncologist and (2) reseach carefully what the outcomes are from the agents being used. This is a highly regulated area of medicine - much knowledge is out there. The difficulty, at time, s is that the choices between alternate therapies is confusing. See a good oncologist...
Chemotherapy. Yes. Although we are much better at treating the side effects of chemotherapy than we used to be able to do, a patient can still die from infection, bowel perforation or another complication.