Another common main character; someone who has been so damaged by their world and their life their storyline generally is about them having to overcome their feelings to be able to progress and cope with the events taking place. How they are damaged though is very much up to you.
In Jeffery Deaver’s ‘Lincoln Rhyme’ novels, the main character has to deal with being paralysed. In a series of books called ‘Jedi Apprentice’, which is about Qui-Gon Jinn and Obi-Wan Kenobi both are damaged and hindered by emotion, especially anger, frustration and fear. In the Hunger Games, Katniss Everdeen is introduced as already damaged because of the death of her father; grief can be a very powerful factor that damages people, as anyone who has suffered it can well tell you and her story only continues to damage her.
It very much depends on what your plot is going to be about in how you go about developing your characters, but generally the story arc is about them overcoming these problems, either through outside help, determination and just sheer basic need to get on with life and get through their problems. What you have to be careful about when writing damaged characters is to remember that people in real life do not get over their problems quickly, and that while a character can appear to have got over a problem, their past can come back to haunt them, even at the most unexpected moment.
Also when writing a character like Lincoln Rhyme, who fall under physical as well as emotional damage, be sure ensure that you do not apply miracle cures to their problems, unless of course you are writing a world where that sort of damage can realistically exist, whether though the advanced medicinal practices or the use of healing magic.
You might also wish to consider the complexity of the character that you are creating. They might not be the most pleasant of people, or like the majority of people they might be very pleasant in certain situations, but very disagreeable in others or when presented with people with whom they have issues in relating with in a pleasant manner. You have to understand your damaged character very well indeed and how they would react in particular situations, especially given the wide range of different problems that a character might have been effected by.
An excellent example of a damaged protagonist is Alex Verus from Benedict Jacka’s fantasy series. He struggles with the horror of his past and the uncertainty he faces in the magical community. He is however very agreeable and helpful with his apprentice Luna, who is damaged like he is by an ill-fated curse. When he encounters his enemies though he can be violent and ruthless if required, whether he is acting to save his friends or simply save his own life.
The variety that you can apply to damaged characters is actually very extensive and can produce some very interesting characters and stories.