My soft spot for fearful dogs started way back with Jake, the beautiful Doberman who started it all. He was under socialized and thrown into a world that he was not comfortable with. My girl Tilley came to me a meek little thing and I only found out later that she was fearful. Sometimes called "shy" these dogs can display their fear in many forms. The range of behavior can go from standoffish to a display of aggression. But a truly fearful dog does not display unless provoked meaning that they don't run out and growl at people for no reason, they don't approach people. Their behavior displya is a response to an approach to them.
A very good example of this is my boy Luke, he is a confident guy who rarely has his tail down but all that changes when we go to the vets. Luke turns into a true Cujo at the vets, so much so that they have asked me to put a muzzle on him(which I do not do). He growls at anything and everything that moves whether it is an animal or person and he tries his hardest to sound very scary. I do not put a muzzle on him because this would only worsen the problem. Once in the examining room and much explanation they are convinced that he will not bite. He has no intention of biting but only to keep them at a distance. This is his response to a fearful situation, keep them away and everything will be fine.
When I meet a dog that is obviously fearful I react immediately attempting to calm their fears. Not by talking to them or trying to reassure them but ignoring them. This is the only way to help a fearful dog. As I have said before our dogs watch us and learn from us so if your dog reacts fearful you must calm yourself and act like whatever the scary thing is, is no big deal. By trying to calm them through petting or verbal reassurance you only make matters worse.
Your response to someone elses dog who is fearful should be the same. Make like you are not there, if you just walked into someones home and the dog is barking and backing up, they are fearful. Do not give the dog eye contact, eye contact is the most important factor. Turn your body sideways to seem less threatening. A full frontal approach is a dominant behavior and not good with fearful dogs.
And one of the most essential ingredients to helping a fearful dog is patience. You cannot get mad at a fearful dog, this makes matters worse as well. Whatever their fear, whether it be a logical fear or not it is a real fear to them and you need to be patient and understanding.
My Tilley came to me with quite a fear of men, she would lurk around the back of the room growling when a man came into our home. Now through patience and exposure she will seek men out over women, it is quite obvious.