Many people have unpleasant dreams of being chased and/or stalked.
If the dreamer has these issues in her daily life, then the fear experienced during the day may be entering her dream state. However, most people that have a dream about being stalked are not stalked in reality.
The dream is symbolic and brings up issues regarding persisting problems or prevailing difficulties.
The dream could represent one side of the dreamer’s personality attempting to catch up with the other.
For example, if the dreamer is doing something hurtful to himself or has a bad habit or addiction, the stalker in the dream may represent that negative part of the dreamer’s personality or life.
The dream stalker could represent your conscious, a prevailing problem, or a goal that you have been putting off and unable to pursue.... The Bedside Dream Dictionary