Michigan State University agreed to pay $500 million to more than 300 victims of sexual abuse by Larry Nassar, the sports-medicine doctor it employed, a sum that is among the largest for victims of abuse and leaves unclear the future financial path for one of the nation’s top public universities.

Officials at the 50,000-student campus declined to say how they would pay for the settlement, and it isn’t clear if they have figured out how. They declined to rule out raising tuition or a state bailout, and they can’t use the university’s...