To bring them to a saving knowledge of Jesus. Pure and simple. Consider the story of the Phillipian Jailer in Acts 16. Everything was going great in his life. He had a family, a good job. Then, 2 radicals who claimed to know the Son of God and who were performing miracles got tossed into his prison. And to make things worse, they spent the entire night singing songs to their God. But then an earthquake shook the ground. All the prison doors flew open and the jailer lost all hope. He knew what he had to do. He must kill himself or face execution at the hands of the Romans. His life as he knew it was over and his family would be ostracized and most likely starve. All hope was lost. He raised his sword, preparing to plunge it into his own heart.... When.... Paul and Silas yelled for him to stop, reassuring him that all he prisoners remained and then they shared the gospel with him. That night the jailer and his entire family were saved and baptized.
So, the next time you see a loved one who doesn't know God begin to suffer beneath a series of tragedies, sit back and pray with great anticipation. Perhaps God is trying to get his or her attention and soon they'll come running into His arms.