Here is an older presentation on how to assess a tree the is hang-up, leaning into another tree that may come down on the trail. It discusses complex situations you could be confronted with and what you should safely mitigate the most complex situations there is today when volunteering in your public forest keeping trails open. This helps you to answer the question: Does the hang up really need to come down or or should you just leave it alone?
This presentation is several years old but is still very good. You can choose to view it below or just download the Power Point or PDF persentaion files.