“I asked everybody for money,” she says, “foundations, people, groups, organizations.” She was able to secure federal grant money to test 2,000 kits and to conduct a study on how sexual assault victims are treated in the criminal justice system. Several years later, the state of Michigan provided $4 million to cover the testing of 8,000 more kits. By then Ms. Worthy had been able to negotiate the cost of the testing down to $490 a kit. But there were still 1,341 untested kits and just two investigators dedicated to the new cases.

In early 2013, a Detroit businesswoman named Joanna Cline saw Ms. Worthy discussing the untested rape kits on a national news program. “I was and am furious” at the oversight, says Ms. Cline, who is the chief marketing officer of Fathead, which manufactures and sells wall decals. When she learned that Ms. Worthy’s office didn’t have enough funding to test the kits and prosecute the resulting cases, she became convinced that this was a solvable problem.

Ms. Cline sent an email to about 200 Detroit business leaders issuing a call to action and laying out her own research. Dozens of other cities had discovered untested rape kits, she found, but they weren’t in the same financial straits as Detroit and so they had more money to process the kits. The city filed for bankruptcy in 2013 and formally emerged from it last December.

Yet Ms. Cline was confident in the local business community. “We probably have the resources to do something to show the victims that they matter, show the perpetrators they’re not going to get away with it and just keep working to make Detroit a safer city,” is how she describes her thinking at the time.

Her email spurred a small corps of Detroit business owners to begin raising awareness and money for the testing of the kits. As public outrage grew, a public-private initiative called Enough SAID (Sexual Assault in Detroit) was created, building on Ms. Cline’s group’s approach to using private fund-raising as a way to address a criminal justice crisis. Enough SAID also sought and received millions of dollars in local, state and federal grant money for kit-testing and investigators.