
As a private pilot it is mostly your choice what situation you put yourself through. To survive being a pilot you need a certain amount of humility and understanding your limitations. Also a lot of planning, including contingency plans on what to do if you get stuck somewhere or if the weather gets bad. You are not an airline, you do not have the equipment and resources they do and you should plan accordingly. This should be part of your training and it is up to you to maintain this as you fly.
If you are interested, a good book on the subject of general aviation accidents and as it relates to private pilots is The Killing Zone, Second Edition: How & Why Pilots Die by Paul Craig. Very readable book.
Additionally, aviation accidents are studied by many people in the industry and there are checklists to follow before and during the flight (IM SAFE [1], PAVE[2]. etc...) that should help you to determine if you even should make the flight. There are also automated tools that calculate based on your experience and the environmental conditions if its a go/no go [3] and if you stick to these things they would make you a very safe pilot. So I wouldn't let a fear of getting into an accident stop you from being a pilot but be smart and follow the rules, set yourself some conservative personal minimums, follow the checklists, and plan, plan, plan and you should be safe.
[0] The Nall Report, the gold standard: https://www.aopa.org/-/media/files/aopa/home/training-and-sa... [1]https://www.thebalancecareers.com/the-i-m-safe-checklist-282... [2] https://www.faa.gov/training_testing/training/fits/guidance/... [3] AOPA used to have a go/no-go decision maker can't find the link.
I believe you're talking about The Killing Zone, by Paul Craig. Highly recommended.
http://www.amazon.com/Killing-Zone-How-Why-Pilots/dp/0071362...
https://www.amazon.com/Killing-Zone-Second-How-Pilots/dp/007...
"This survival guide for new pilots identifies the pitfalls waiting inside the killing zone, the period from 50 to 350 flight hours when they leave their instructors behind and fly as pilot in command for the first time. Although they're privately certified, many of these unseasoned aviators are unaware of the potential accidents that lie ahead while trying to build decision-making skills on their own -- many times falling victim to inexperience."
