Meaning of dreaming of running away from someone means something bad in near future as per dream interpretation.
If you simply dream of someone chasing you then it means that soon you will enter into a phase of life where it will be impossible for you to determine between what is right and wrong. Basically you will be confused as to what you need to do. You need to take advice of good elders or experienced people.
Dreaming of you running away from someone you know means that you will be cheated. A person whom you have trusted will turn out to be a fraud. It also means your lover is not a lamb but a cunning fox after body pleasure or wealth.
Dreaming of you running away from someone and you falling means you will accept defeat in something without trying and this is a big mistake.
Dreaming of some running after you and catching you means a secret of yours will be exposed. All illegal activities that you were indulging in will be caught.