If you consider that life happens on a continuum of actions, being a prisoner of fear is a very real thing. What I mean is, consider how a 130 lb woman can lift a car when she believes her child is underneath; emotions drive actions. In psychology, fear is considered to have a physical and a psychic reaction for individuals. In the physical state, one can be paralyzed by the mention of a spider, or nearly being run over by a bus. In the psychic state, thinking about a major quiz or test, or considering being rejected by a person you admire and/or love, can make you equally paralyzed.
I used the last analogies to explain the control that emotions have over actions and perception. If someone is deeply afraid of something, they cannot move or act to release themselves from the fear. Scientifically, Darwin explains fear as a repelling emotion. When fear is sensed, the body reacts to protect itself. To this end, someone can feel cognitive dissonance, or in plain terms, someone can believe that they need to act one way, but be totally incapable of acting in that way because of the fear. Thus, they are a prisoner of fear. The fear controls them to the point that they physically and psychically cannot act.
A person could be a prisoner of fear when they are so scared of something that they literally cannot act. It could be that they are frozen with fear and can't move, kind of like a deer in the headlights. In that case, the fear is holding them to a specific spot or location; that sounds a lot like a prison cell.
It wouldn't have to be so drastic, though. A person could be a prisoner to their fear in much subtler ways. Let's say that someone is terrified of flying. That limits potential travel destinations. Sure, driving or going by boat, bus, or train is an option, but all of those methods might take much longer; therefore, they may not be viable options. That person is inhibited from doing something because of their fear.
There is a medical condition that involves being afraid to leave your own home. That makes the home both a sanctuary and a prison at the same time. Either way, it's fear-driven. The name of the psychological disorder is agoraphobia.