AT LAST, they know.

Franchesca Alvarado's family now knows that she will never come home.

She will no longer sing her daughter Janiya to sleep. She will not enroll at Community College of Philadelphia, where she was to major in criminal justice. She will not meet her sister Mia Casteing for play dates with their kids at Piccoli Playground in Tacony Park. She will forever be 22 years old - her age when she vanished on March 17, 2012.

Franchesca's family says they learned this week that her DNA matches the DNA from a severed foot encased in a sneaker that washed ashore in August at New Jersey's Corson's Inlet State Park. (Although New Jersey State Police have not officially confirmed the DNA match, the family says a police source told them it is Franchesca's).

"It's closure. But it's horrible. Cheka's gone," says her sister, Alma Rios, using Franchesca's nickname.

So her seven siblings will no longer need to plaster the Atlantic City Boardwalk with posters asking for help to find their youngest sister - a task they did so often they now know casino staffers by name. Nor will they need to hang posters in the Kensington neighborhood where Tracey Williams was last known to live.

He's the man, decades older than Cheka, who took her to Atlantic City the March night she disappeared. He returned alone, saying Franchesca decided to make her own way back to her apartment in Hunting Park.

When Franchesca vanished, Williams cooperated with police, says Lt. Harold Lloyd of Philadelphia East Detectives. But when Williams was asked to take a lie-detector test, he refused and hired a lawyer. Police now have information that Williams has left the area, Lloyd says.

For 18 months after Franchesca vanished, there had been no sign of her - no phone calls or credit-card activity. She didn't show up for Janiya's birthday, an event she never would've missed, or for Mother's Day. There was nothing until seven weeks ago when a fisherman found that sneaker - an Adidas ADI Rise 2 high-top sneaker, size 5.5.

"We knew right away it was Cheka's," says another sister, Tina Diori, describing how sister Mia screamed in grief when she saw a photo of the sneaker broadcast on the evening news. The family had teased Franchesca about the shoes being boyish and ugly when she bought them. Mia immediately contacted New Jersey State Police, who began the process of DNA testing.

The foot, whose toes still had traces of nail polish, was badly decomposed, says Lloyd, who oversaw Franchesca's missing-person case. Perhaps that's why it took almost seven weeks for the DNA tests to be completed.

But when New Jersey State Police asked for additional swabs from Janiya's mouth (which would contain traces of Franchesca's DNA), the family knew that the results would break their hearts.

"Now we have to figure out how to tell Janiya," says Tina, with whom the child lives. "For 18 months we've been saying that Cheka is at work."

Franchesca's death is a shattering end to the life of a young woman who had survived a bleak childhood. She had struggled with her father's absence (in prison) and the death of their mother, who passed when Franchesca was just 9.

"Before she died, she told me to always look after Cheka," said Mia, who is 4 years older than Franchesca and whom I interviewed shortly after Franchesca went missing. The two girls stayed with various family members and others until they reached legal age.

"We were the youngest and she wanted us to stick together," said Mia.

During that dark period, a relative sexually abused both girls. It took a long time to come to terms with that. Healing together tightened their bond. So much so that Mia, whose life has been consumed by grief since Franchesca vanished, was unable to speak to me this week.

"She is heartbroken that Cheka is dead," says sister Alma. "We all are. But they were best friends."

She pauses. It's a struggle, she says, to use the word "dead" to describe the sister she had wildly hoped was still alive, even though common sense told her otherwise.

"Every morning, on my ride to work, I would wonder, 'Is this the day we'll get the call that they found her body?' " she says. "And every time it rained, I would wonder, 'Is it raining on Cheka's body? Is she out there?' "

And now that Cheka is gone, Alma will need a new routine to help her sleep.

"I hung glow-in-the-dark star stickers over my bed after she went missing," says Alma. "I would pick one star and stare at it and think of Cheka. It was the only way I could fall asleep."

New Jersey State Police are investigating the death, says spokesman Sgt. Adam Grossman. The department has been aided in part by Philly's Lt. Lloyd, who met for hours with investigators to turn over the copious records he amassed when Franchesca was characterized as a missing person.

"We want to find the rest of Cheka's remains," says sister Tina, who is grateful that a New Jersey cadaver-diving team has volunteered to search the waters of Corson's Inlet this weekend. "I want the fisherman to show us the exact place he found Cheka's foot."

Tina has spoken by phone with the fisherman and his wife (she declined to identify the couple until the family has chance to meet them in person, saying only that they live in Lancaster, Pa.)

"Oh my God, they were so sweet and kind," she says. "The wife even cried with me when I thanked them for helping us find Cheka."

But real closure, she confesses, won't come until they know precisely how and why Franchesca died.

"She should be here," she says urgently. "We miss her so much. Janiya needs her. We won't rest until we find out what happened."

Phone: 215-854-2217

On Twitter: @RonniePhilly