HOW WELL DO THE WOUNDED FIT INTO THE CHURCH?

In most of the churches I know, then there are people who have troubles for sure, and they definitely know of the pain and strife of the world. But often I wonder how well does the person who has lived a hellacious childhood, or lived with evil done to them for a prolonged period of time, fit into certain churches? Often I think we aren't a place where these people feel comfortable. And these are people who are longing to know that there is a God for them to cry out to. But many churches don't reach these people because they have major walls around their hearts. What we wounded need when we have such a hard heart is to have someone pursue us with the relentless unending love of Christ, and it may take years for the gospel to penetrate. I remember learning from someone along the way in my Christian walk that I would pick someone good to invest my life into, by choosing someone who is FAT - Faithful, Available, and Teachable. However, many severely wounded do not appear as FAT and therefore we would not continue to invest in them. Then the severely wounded fall by the wayside, never getting to hear about the love of Christ for them. Do you agree?