Well, that doesn't happen. Those people who have nobody to talk to are more likely to be anxious and depressed. Several other researchers have shown that when people are seriously ill one of their biggest problems is that other people won't talk to them, and the feelings of isolation add a great deal to their burden. In practice, if a major anxiety is occupying someone's mind, that person frequently finds it difficult to talk about anything at all. One of the reasons for which people bottle up their feelings is shame.
Many people are ashamed of some of their feelings - particularly of their fears and anxieties.
One of the greatest services you can do for your friend is listen to her fears and stay close when you've heard them. By not backing away, you show that you accept and understand them. This will, in itself, help reduce the fear and the shame, and help the patient get her sense of perspective back. So for all these reasons, you have everything to gain and nothing to lose by trying to talk to, and listen to, someone who's just been told that she or he has cancer. Now, starting a conversation in these circumstances often feels very awkward and embarrassing.