There is much philosophical literature on the duty to rescue. Individuals who encounter and could save, at relatively little cost to themselves, a person at risk of losing life or limb are morally obligated to do so. Yet little has been said about the other side of the issue. There are cases in which the need for rescue could have been reasonably avoided by the rescuee. We argue for a duty to take rescue precautions, providing an account of the circumstances in which it arises. This novel duty has important implications for public policy. We apply it to the situation of some of the uninsured in the United States. Given the US clinician's duty to provide emergency care to all people regardless of ability to pay, some of the uninsured have a moral duty to purchase health insurance. We defend the duty against objections, including the possibility that a right to rescue can be waived, thus undermining a duty to take rescue precautions, that the duty of many professionals is voluntarily incurred, and that a distinction between actively assumed and passively assumed risks matters morally.