Katrina cut a destructive swath through the Gulf Coast, upending lives and causing huge dislocation. Yet for some New Orleanians, the hurricane also offers a glimmer of a silver lining. New Orleans has for years been known as one of the nation's murder and drug capitals. Many evacuees, especially the unemployed and those with low-paying jobs who don't own property, see moves elsewhere as opportunities for a fresh start.

The transition likely will be difficult. Many evacuees lack basic job skills, have no college degrees or no high-school diplomas. Many have never even left New Orleans or their neighborhoods.

Hundreds of evacuees have approached the Red Cross travel desk here asking to be taken out of the area. "People come here and say, 'I want to go to Minneapolis. Or, 'I have a relative in Texas, just get me there and I can start all over,' " says Deborah Thomas, a volunteer managing the desk. Other volunteers say similar scenes are playing out at shelters across the region.

Earlier this week, a group of women huddled around a bulletin board here scanning postings for jobs and free housing in California, South Dakota and New Jersey. Many couldn't point out some states and cities on a map. Ms. Singleton had looked at the same bulletin board for her chance at a new life.

That chance came in the form of Tanya Thornbury, an artist who lives more than 1,000 miles to the north in Montevideo, Minn. On Monday, Ms. Thornbury sat down at her computer and, using a search engine, found a link to the River Center. She sent an email offering a single mother with a child space in her home for a year free of charge.

Ms. Thornbury, 36, and her partner, Tracey Thornbury, 38, have four children; the eldest serves with the Army in Afghanistan. They live in a four-bedroom Victorian on a tree- lined street in Montevideo, a quiet town with 5,346 residents about a three-hour drive from Minneapolis. Tanya Thornbury stays at home with the kids while her partner drives an 18-wheel semitrailer. Ms. Thornbury says she was moved by the TV images showing people screaming outside the New Orleans Superdome.

"I see how poor those people are," Ms. Thornbury says. "To open your homes in places where people can prosper, it's wonderful."

Soon after Ms. Thornbury's email popped up at the River Center, it was printed out and tacked to the bulletin board. The posting caught the attention of Ms. Singleton, a sturdy woman in hoop earrings and a white bandanna. Ms. Singleton, who has a high-school diploma, worked a succession of menial jobs in New Orleans. Her six children range from 2 years old to 16. Before the hurricane, she had never left New Orleans.

Ms. Singleton arrived at the River Center on Monday after being rescued by boat from her Algiers neighborhood, across the Mississippi River from downtown New Orleans. She had been stranded for seven days and her apartment was destroyed. Five of her children had been sent with her mother to Texas before the storm. Her 16-year-old daughter, Brittany, who had initially stayed with Ms. Singleton to guard their home but later left, was missing.

"It's by the grace of God I got out," says Ms. Singleton, who gave her savings to her children before the storm. "I don't have a penny to my name," she says. "All this is strange." As of yesterday, there was no news on her missing daughter. Ms. Singleton says she is worried sick about Brittany. She has put her name on a missing person's list and is calling her mom in Texas everyday to find out if Brittany has showed up there.

Soon the phone in Ms. Thornbury's house was ringing. "I'm interested in your email," Ms. Singleton recalls telling her.

Ms. Thornbury told Ms. Singleton she was welcome to come live in Montevideo, a town where "you don't even see people pulled over." Ms. Thornbury says she "didn't care anything about who she was. I just wanted her to be safe."

Though her ad offered to take just one child, Ms. Thornbury plans to accommodate Ms. Singleton's children as soon as possible. "It'll be a squeeze but you know, you can't pick and choose which kid can come. We were going to refinish the attic anyway."

But Ms. Thornbury worries Ms. Singleton, who is black, will have culture shock. Montevideo has very few black residents. Ms. Singleton says she told Ms. Thornbury, "I get along with anybody -- Creole, white, black. For me it's no problem." Ms. Thornbury also made it clear her partner is a woman. "I don't care," Ms. Singleton said.

Ms. Thornbury told her family Ms. Singleton would soon be arriving. Ryan, 12, the Thornburys' second-oldest child, immediately offered his bedroom. Ms. Thornbury went to the local Wal-Mart and bought a bathrobe, pajamas and sandals for Ms. Singleton. She had a friend get Ms. Singleton a job application from a local turkey-processing factory and talked her up to a Wal-Mart manager.

Ms. Singleton says she'd take any job she could get and, "if things work out, I'm going to college." She says she wants to be a nurse or a cosmetologist. "I like doing hair -- if I had some clippers, I'd be cutting these boys' hair, for no charge," she says, pointing to some boys nearby. "If I can just get up, get a job or something, I'll take it."

Just after 5 p.m. Tuesday, Ms. Singleton heard her name called over the River Center intercom. A flight had been arranged for her to leave that evening for Minneapolis-St. Paul, one of nearly 150 flights from Baton Rouge to points across the country that day. She was frightened about flying for the first time and briefly considered asking if she could go by bus. "Nah," she says. "This is my chance."

The airplane allowed each evacuee no more than 50 pounds of belongings. Ms. Singleton threw away some of her kids' clothing and her own underwear. She kept her bedsheets folded neatly in a plastic bag. "I don't want to get up there and have people think I don't have anything," she says.

But as of yesterday afternoon, she was still waiting for a flight or bus to Dallas, Houston or Atlanta to connect to Minneapolis. In tears, she called Ms. Thornbury to report her flight had been postponed for the second or third time. The women have yet to meet, but Ms. Thornbury says they have already bonded. "She tells me she loves me every time she calls," Ms. Thornbury says.

• Read part two of Steven Gray’s Wall Street Journal series about the human toll of Hurricane Katrina’s aftermath.