I had a collegue at work who was very much like your friend. She was very withdrawn, very cynical about life and all that because she made some bad experience with people she trusted in her youth. By winning their trust you can be something like a friend to them but beware:
1) They will stick to you since you are their only friend. This gets annoying very fast.
2) They feel tricked and cheated by you very fast and snap back into their 'the world is bad, nothing good comes from other people' behaviour scheme.
Most of these people just need a good relationship. Someone who's around and can be there all the time, listen to their problems and letting them feel that there's someone who needs them. Just a normal life.
~Marimmar