A disease is a particular abnormal condition that negatively affects the structure or function of all or part of an organism, and that is not due to any immediate external injury. Diseases are often known to be medical conditions that are associated with specific symptoms and signs.
Depending on the 10 Great Families, they have diseases that they are prone to or immune to. For some Great Families, there exist some critical diseases that are hereditary. E.g. Yeon Yihwa is immune to most of the diseases, but from time to time she gets light cold. It suits her since she has fire quality.
There is no Cancer Disease in the Tower. But there are cases like a person develops an allergic reaction to Shinsoo as they get older, and the cells start to function improperly due to it, which is quite similar to cancer.
The chance of someone getting a disease becomes higher when the person does a poor job in managing their own health. If someone dies of old age in the Tower, this is usually the case.