Bleeding is not a "normal" part of cancer, and any bleeding should be brought to the attention of your loved one's healthcare providers immediately. If your loved one is facing a surgery, the oncology nurse and physician should tell you what to expect afterwards, such as drainage from the surgical site.
Surgeries aside, if you notice an occasional nosebleed, gums bleeding after your loved one brushes his or her teeth, or a sore that isn't healing, bring this to the attention of your loved one's healthcare providers. Any area of bleeding is a potential portal for bacteria to enter the body and cause infection. In addition, bleeding could signal other problems that need to be addressed, such as a low platelet count. Identifying the underlying cause of bleeding is an important first step in managing it.