Spiritually the image of being chased or pursued suggests either fear of our own actions, or is a play on words, as in ‘chaste’, i.E. Trying to preserve our innocence.
Psychological / emotional perspective: Being chased by shadows shows the need to escape from something previously repressed, such as past childhood trauma or difficulty.
To be chased by an animal generally indicates we have not come to terms with our own passion.
Material aspects: Dreaming of being chased or of trying to escape is perhaps one of the most common dreams; usually we are trying to escape responsibility, our own sense of failure, fear or emotions we can’t handle.
Gives gender - specific: It is not unusual for a woman to dream that she is being pursued in dreams.
The implication is that she has something special which she does not wish to relinquish.
If a man is being chased by a woman or that which he cannot identify then it is usually in response to his fear of being ‘consumed.’