Primarily the Zakat is to help the poor and needy Muslims. Similarly, if you think that by giving Zakat, you can win the heart of a misguided Muslim and bring him back to Islam, then Zakat can be given to him. You help him with Zakat and remind to follow his religion. Perhaps by this good treatment he will come back to Islam. Very often we Muslims give da'wah to others, but we do not take care of their physical and financial needs.
Poverty sometimes pushes people to neglect their faith.
However, we should also be careful in giving Zakat. We should not give Zakat to any one who may use it to indulge in sins or to rebel against Allah and His deen. Yes, it is permissible to make claim and to receive settlement money for personal injury or property loss due to auto accidents. A Muslim has to be honest whether dealing with Muslims or non-Muslims. I have earned this profit sharing for the last five years in certificates, not in a form of money.