Thousands of children are missing across the country. The longer they are gone, the smaller the chance they will be found alive. So when three women who had been missing for a decade or more emerged from the house where they had been held captive, it provided an extraordinarily rare happy ending.
"I would definitely say it was a miracle," said Kelly Murphy, who founded Project Jason, after her own son vanished, to help other such families.
Murphy had worked with two of the Cleveland families while their daughters were missing. After they were found, she heard from many others who are still searching.
"The general response is that it gives us all hope," Murphy said. "I'm in the situation, too, with my son almost missing for 12 years without a trace and without clues. It definitely gives us hope that there is a chance. If it happened to those girls, it can happen to us."
"To have hope helps you get through each day, hope that there's a good answer instead of the answer that nobody wants. It just helps you keep going, because it's very difficult to have to live with ambiguous loss."
But how much does it help to hope for a miracle, which by definition is almost impossible?
Some, like Murphy, need to keep that spark alive, however small. Others, like Jody Himebaugh, need to protect their emotions.
Himebaugh knows about what happened in Cleveland but has avoided the details. His son Mark disappeared in 1991 at age 11.
"Every time I watch this kind of stuff, it rekindles the last 23 years," he said. "All it does, it just gives us hope again."
For Himebaugh, hope hurts. Whether hope is more painful than saying a permanent goodbye — that's impossible to figure.
"For the past 23 years, I've been happy for the families over that time who have recovered their kids, dead or alive," he said. "At least they've got closure. My biggest fear is I'm going to go to my grave and never know what happened to Mark, and why."
The flip side of that fear is hope — and the loved ones of the missing hold tight to every glimmer. Advocates and others often speak of persistence, of keeping missing children's images in the public eye, of always working to make sure the public stays alert for the one tiny detail that could end a family's agony.
"What an amazing time to be talking about hope, with everything that's happening," Jaycee Dugard, who was missing for more than 18 years before being rescued, said this week at an awards ceremony where she urged the audience not to give up on missing children.
In Cleveland, several religious leaders spoke on that theme Wednesday. Catholic Bishop Richard Lennon posted a video message urging viewers to pray that missing people "may have the strength of the virtue of hope and that their families also may never give up hope."
After a prayer gathering on the block where the women were found, the Rev. Larry Harris of Mount Olive Missionary Baptist Church said, "There's a hope that many, many more will be coming back home."
On the block where the three women were found, Tonia Adkins was wearing a T-shirt printed with the face of her missing sister, Christina Adkins. Cristina vanished in 1995 at age 17, four blocks from the house where the women were held captive.
The arrests of three brothers has given the Adkins family hope for Christina, but has also stoked the dread that has been part of their lives for 18 years.
"I do believe that they're gonna break open some cases," Tonia Adkins said. "I'm scared that I'm gonna get the news that my sister's not alive."
The space between hope and resignation is a difficult place.
"It's an absolutely terrible predicament to be in. I can't imagine what families go through wondering — just the lack of knowing," said Bob Hoever, director of special programs with the National Center for Missing and Exploited Children.
He recommends hope and sees this as the powerful lesson of the Cleveland case.
"I believe this is a tremendous boost to families giving them hope, that we should never give up looking for their children," Hoever said. "The National Center never stops looking for a missing child. As long as they're missing, we will continue looking."
But Sherry Hamby, a psychology professor at Sewanee: The University of the South who studies the victimization of children, said some families can become frozen in time at the point their child disappeared.
"At some point, after so many years have gone by, there's a lot to be said for closure," Hamby said. "It's just not a natural state of being for humans to be frozen in this time, waiting. We can't stay in that kind of limbo forever."
The most difficult decisions, Hamby said, can involve what seem like mundane details.
"Are you going to pack up that child's things? Are you going to convert that room to another use?" she said. "I think the need for psychological closure just is necessary because of the concrete limitations that we are facing. It's just hard to go through life trying to not make any changes."
Murphy, of Project Jason, knows families who have chosen to believe their missing child is dead, and she does not begrudge them that choice.
But Murphy holds onto hope, "because it keeps us focused on the future."
"It's just unfortunate that in our case," she said, "we don't know what the future holds."