Fifty-one years after Lyndon Johnson declared “unconditional war” on poverty in his first State of the Union, anti-poverty workers allowed themselves a small celebration Wednesday, cheering an assertion that Connecticut is on the verge of eliminating chronic and veterans’ homelessness.

“This is not a distant dream any longer,” Gov. Dannel P. Malloy told an audience in Hartford, announcing that Connecticut was one of a half-dozen states chosen for Zero 2016, a final push to win one battle in the long war on poverty.

Connecticut has about 1,000 chronic homeless, including veterans, down from 10,000 a decade ago, a reduction that anti-poverty workers attribute to a smarter national approach and increased resources committed locally by the Malloy administration.

Reaching “zero,” of course, does not truly mean an end to homelessness, a time when the shelters can close. A United Way report last fall found that 474,445 residents here struggle to afford the basic necessities of food, clothing, housing, medical care, child care and transportation.

Homelessness for many of them can be a layoff or illness away, said Lisa Tepper Bates, a former U.S. diplomat who is now the executive director of the Connecticut Coalition to End Homelessness. They are on the “knife’s edge,” she said.

“Ending homelessness doesn’t mean preventing anyone from ever becoming homeless again,” said Alicia Woodsby, executive director of the Partnership for Strong Communities. “It’s about creating a system that knows how to get them out quickly and prevent them from returning. There will be an end to homeless when it’s rare, brief and non-recurring.”

Catherine Zall, the executive director of the Homeless Hospitality Center, who is in the nightly business of trying to match pillows to people as temperatures drop, smiled when asked what she thought about an end to homelessness, by whatever definition.

“I’m so in the day-to-day of it, I don’t put my head up enough,” she said.

But Zall, who drove to Hartford to applaud Malloy’s announcement at a ceremony at the Lyceum conference center, said the progress was real enough and worth celebrating.

“I think it’s really important, because people are so skeptical about the ability of government, non-profits,” Zall said. “People think, ‘Oh, these investments don’t matter.’ We can, by investing significant but not extraordinary amounts of money, really make a difference for people who are really at the very bottom.”

The efficacy of Johnson’s war on poverty is debated today, but it produced lasting programs, such as food stamps, Medicare and Medicaid, Head Start and VISTA, which have demonstrably reduced poverty rates.

But Johnson aimed higher: “Our aim is not only to relieve the symptoms of poverty, but to cure it and, above all, to prevent it.”

Zall is familiar with the difference between relieving the symptoms of homelessness and preventing it.

She said the Homeless Hospitality Center – “Hospitality is our middle name,” Zall says with a smile – opened in 2006 while New London was struggling to maintain its social services. A man died in the woods after a city shelter had closed for the season.

The center’s hospitality in its first year was little more than rolling out mats on the floor of a heated building.

“Putting mats on the floor is not an answer to homelessness. It’s a start. And we did what we had to do,” Zall said. “But I think we are now really starting to understand how to move people from homelessness to housing.”

The approach today is holistic, one geared to prevention of chronic homelessness, not merely solving the immediate problem of providing a warm place for the night, Tepper Bates said.

“We’ve learned a lot nationally,” she said.

Many shelters today provide screening, finding medical help and supportive housing for those with mental disabilities. For those whose homelessness is primarily the result of a financial setback, the goal is “rapid re-housing,” offering aid that stops a downward spiral that can be more difficult and more expensive to cure.

“It’s not what shelters did just a few years ago,” Tepper Bates said.

The Malloy administration has played a role by giving the front-line workers greater options by investing in supportive housing and public housing, including bringing long-vacant affordable apartments back into the housing market, she said.

“This governor, this administration and their understanding of the importance of this issue and their willingness to invest in the solutions have been critical to the progress we’ve made against a tough economy at a difficult time,” she said.

On Wednesday, Malloy also announced that the state Department of Mental Health and Addiction Services was providing $1.1 million to 15 non-profit agencies for in-home services to 176 persons who have experienced chronic homelessness.

To be chronically homeless is defined by the U.S. Department of Housing and Urban Development as living in a shelter or a place not meant for human habitation “for at least one year or on at least four separate occasions in the last three years,” while being diagnosed with a serious mental illness, addiction or chronic physical disability.

Tepper Bates said the shelter workers know that eliminating chronic homelessness would be a important milestone — but only a milestone.

“I think its pretty exciting, but there’s plenty more to do after that,” she said. “We’d like to see efforts to help them keep climbing the ladder. Ending homelessness is one step. That’s one way I’d look at it. There’s plenty more work to do after that.”