Honestly, I don't think this is a problem specifically for the person with the terminal illness. So much of the difficulty comes from everybody else. American culture does not prepare people to face death, either their own or of loved ones. So a lot of my energy goes in to helping other people manage their feelings at a time when I don't have energy to spare. I want other people to take LSD or do Zen retreats or serve at a hospice or whatever they need to do so they can manage their own death anxiety.
Speaking of which, I strongly recommend the "ring theory of grief" article. The gist is that if bad shit is happening to somebody, you help them rather than imposing on them. It sounds obvious, but I promise that it's unfortunately rare. Here's the article: http://articles.latimes.com/2013/apr/07/opinion/la-oe-0407-s...