As followers of Christ, we must respect God's creation of all people, and see them not as problems to be ignored or hidden away. Rather, we must see them as mirrors of our own brokenness, and as divine windows through which we can catch glimpses of God's grace. We must do whatever we can to respect God's image in even the most broken and twisted lives. Even the least of these carries intrinsic dignity and worth.
When we begin to do for the least of these what David did for Mephibosheth, and what Jesus called his followers to do, we discover this: we are the broken and the needy. They. Are. Us. Perhaps more openly and undeniably, but all the same, they remind us of our true state before God. That is the gift they bring to God's people.