Sadly, from what I've read so far it turns out that this sort of worldview is a slow death. It's because the people who silently worry what they will do next are constantly under stress, animals in the wild. They have no control. It's a slow, lurking, chronic stress, barely detectable yet always there. The stress-response system ("fight or flight") is constantly running, which means the higher parts of the brain are not running properly, like calm reasoning, deliberation, judgement. It pains me to think of it. We all know these people.
I actually had the opposite opinion for a long time. Previously I thought that the rich people at the top were the most unhealthy, stressful, unhappy people in the world. Based partly on my religious views and partly because I wasn't rich, I would say "I never want to be rich...they are miserable." But then I read about the major studies that were conducted in England and other places, which clearly conclude that the lower you are on the social ladder, the more stressed you are, and the higher you are, the less stressed and more happy and healthy you are. It turns out Jesus was right when he said "Woe unto the rich, for they have their reward." In other words, they might have problems in the next world (due to love of money), but in this world they do pretty damn well. The book Born For Love comes to mind too.
It's human nature to fear and this is one example of it. Yet, as all great religions and moral philosophers say: it's human nature for us to transcend human nature. First, will power. Stop saying "they." Catch yourself. Start there. I've done it. In my job, I always say "we" made a decision, whether I agree or not (it's pretty easy, the library is one of the best places to work). We passed Obama Care. We went to the moon. We cloned a sheep. Get it? It feels great and sounds right.
Second, go read Meditations by Marcus Aurelius. If you don't think ideas can change your life, keep reading--eventually you will find what's meant for you. Stoicism is perhaps the best philosophy to deal with the unpredictability of life, which says: (1) never worry about things outside your control (because that's stupid), and only worry about things within your control (that's smart); (2) now conquer and overcome those things within your control; (3) now your life is, by definition, free from worry. Everything else is accepted with grace and all things are seen as a beautiful play of events, a gift from God or Destiny or Chance. The events that led to meeting my wife were random, sad, beautiful, and ended in one of the best decisions in my life. I took them all with stoic grace.
Third, if things get really bad--and sometimes they do--try faith. Religion, as Jesus said so poetically in the Sermon is the Mount, is really for the lowly, the down trodden, the poor. When the world shits on you, when you don't have a family to love you, when your greedy employer downsizes you, when you become ill and your luck runs out--only God is left to love you. Or despair. Both are understandable. This is why Aristotle thought that the good life required a little bit of luck.