Detroit's reputation precedes it: its economic decline and apparent decay regarded as a warning sign for modern civilisation. But one Motor City native isn't buying this narrative. "Detroit is a wonderful place," enthuses Kym Worthy. "Yes, it's half the size it once was, and yes it has had its share of crime, but you visit downtown, midtown, many of the neighbourhoods in the city, and you would never believe that it's the city you've heard about on the news," says the 56-year-old.

It takes an extraordinary woman to be this upbeat given the circumstances she is describing, but extraordinary is exactly what Worthy is. For the past decade, Worthy has been prosecutor of Wayne County, Detroit, making her the chief law enforcement officer for the county's largest city. As a lawyer she has built a strong reputation for tenacity, not least in 2009 when she ambitiously – and successfully – pursued Detroit's then mayor Kwame Kilpatrick on corruption charges. As the first African-American woman to become prosecutor of Detroit, Worthy knows a thing or two about beating the odds, a trait she possibly inherited from her army officer father, the first African-American to graduate from West Point military academy in the 1950s.

Not for nothing did Essence magazine describe her as the "toughest woman in Detroit", a moniker which sprung in part from her actions one afternoon in August 2009, when Worthy's staff made a startling discovery.

"I was sitting in my office one day when assistant prosecutor Rob Spada came in and told me he had been doing an inventory of Detroit police department evidence," she explains during a rare break in her schedule. "There was this warehouse of old evidence that none of us knew about. And that's where he found the rape kits."

A rape kit is a sexual assault kit used to take and preserve forensic evidence through DNA swabs following an allegation of rape. Spada had stumbled across approximately 11,000 of these kits lying in random order, uncatalogued, unattended and uninvestigated.

Worthy's initial reaction was one of disgust and she immediately contacted the then police chief. She faced a lack of interest "until a local reporter picked it up, and then the whole thing blew up".

With the commissioner on board, Worthy soon assembled a team of volunteers to begin the lengthy process of cataloguing the rape kits. "It took us six to nine months to build a database; we had to open each one of the what we now know is 11,304 kits. There was no previous nexus to go on, so we started from scratch. We had volunteers going over these kits for hours each day (without opening the evidence itself), using any identifiable information about the assault to build a database. We combed through years of records to try to match the kits with any police records there may have been. And at times we were literally blowing off the dust of old books that they used to keep back in the day to record the cases."

The hard work of Worthy and her volunteers attracted national attention, and she was awarded a federal grant of $1.5m to continue the work. She began working with various state departments, universities and private sector entities to begin the long and toilsome task of solving some of these crimes. And it worked.

Audrey Polk was assaulted in 1997 when a man broke into the house and raped her in front of her two children. Hers was among the untested rape kits discovered by Spader, and 12 years later prosecutors knocked on her door and explained that her case was finally being looked into. "I was in shock. They said, do you still want to prosecute? And I said, certainly, absolutely, yes I do," she recently told NBC news. Polk's attacker was found, charged and, after an arduous trial, found guilty. He was sentenced to up to 60 years in prison.

A particularly horrifying case involves Shelly Andre Brooks, who is currently serving life in prison without parole for the sexual assault and murder of at least seven women. Through a DNA sample in one of the rape kits, Worthy's team were able to link Brooks to the rape of a woman in 2006 whose kit had never been examined. Worthy states that Brooks went on to kill at least one other woman in 2007 and police believe he may responsible for several other murders.

Untested rape kits are not a phenomenon exclusive to Detroit. Memphis, Cleveland and parts of Texas (where the indomitable Senator Wendy Davis just helped secure funding to tackle the problem) are all trying to deal with a backlog of untested kits, while officials in Chicago are responding to claims that untested rape kits dating back to the late 1970s number in their hundreds.

Time and money are the given reasons for so many kits being disregarded; it costs $1,500 to test the kit, and more if a conviction is sought. But Worthy believes that institutional attitudes in the police force also contributed to so many cases being ignored. Part of her current work is looking at "the way women are handled as victims of sexual assault, from the time they report it to the time of prosecution. Because we've found there has been some very bad treatment [of them]."

She should know. While at law school in Indiana, Worthy was sexually assaulted while out jogging. Though she reported the incident to her school she did not report to the police. "I was young, at the beginning of my career. I didn't want to do anything to derail that. It is not easy for women to shake off the sense that there is a stigma involved with sexual assault. That is something I want to work on changing."

Since 2009, 1600 rape kits have been investigated by Worthy's team, a staggering 37 serial rapists have been identified and 13 cases have been brought against suspects as a direct result of Worthy's endeavours. "It sounds like a small amount, I know," says Worthy, "but we're pushing for more funding." As a mother of one teenager daughter and recently adopted twins, now just four-years-old, you wonder when Worthy has time to sleep, let alone commit extra hours to a project that is already running on goodwill and scant resources as it is.

In September, the $1,5m grant will run out. Private donations, like that from the Joyful Heart foundation, a charity started by actress Mariska Hargitay, who plays Olivia Benson in Law & Order: Special Victims Unit (where storylines revolve around cases of sexual assault), go only some of the way to funding Worthy's work. She needs a lot more money to keep going.

It's surprising to learn that someone as dogged as Worthy didn't much fancy the job of prosecutor. "My view of prosecution was very skewed. I didn't want to be the contributing factor in putting other African-Americans in jail. But I realise now I was wrong. The prosecutor is the gatekeeper of the people. It's very important to be on the side of the people."

• End the Backlog, a charity affiliated with the Joyful Heart Foundation: endthebacklog.org accepts donations. Donations are also accepted through detroitcrimecommission.org.

• This footnote was added on 28 August 2013. After publication of this article, the Wayne County office has been in touch to clarify that Detroit is the largest city in Wayne County, Mayor Kilpatrick was prosecuted in 2009 not 1998, as was previously stated, and that Detroit does not have police commissioners but police chiefs. In addition, the following corrections were made: 1,600 rape kits have been tested, not 600, and the original rape kit grant was $1,515,000, not $1m. The correct spelling is Rob Spada, not Spader.