I agree with Plymouth. Except for cancers caused by some viruses, cancers cannot be spread person to person.
Your question is very interesting because it points out how different cancer is from what most people think of as a "disease". If anything, it's the cancer patient who is at risk. Cancer and cancer therapy wipe out or interfere with the immune system. This means that people with or being treated for cancer are extremely susceptible to contagious diseases, and - if they should catch such as disease - have the most severe form. For example, chicken pox is potentially deadly to a cancer patient.