SAN FRANCISCO — A plan to combat panhandling and animal shelter overcrowding in one fell swoop could be described as killing two birds with one stone. But in the city of St. Francis, no one talks about offing feathered friends.

Instead, the latest municipal innovation, which will pair beggars with problem puppies to make life better for both, is simply called WOOF: Wonderful Opportunities for Occupants and Fidos.

In August, carefully selected dogs from the city shelter will be given to screened and trained formerly homeless people, who will foster the animals. The temporary guardians will receive a weekly stipend of $50 to $75 and must agree to jettison their cardboard signs.

“I can’t make panhandling go away,” said Bevan Dufty, one of the plan’s architects. “But I can make a better offer.”

Dufty, a former county supervisor, is San Francisco’s director of HOPE, Housing Opportunity, Partnerships and Engagement. His plan addresses two serious problems in the city.

In a tourism bureau survey released last year, 25 percent of visitors polled said their biggest complaint about the city was encountering the homeless people and panhandlers, eclipsing responses about the weather and traffic.

And since the nation’s economic recession began, said Rebecca Katz, director of Animal Care and Control, the city-run shelter has seen a significant jump in abandoned dogs.

“We find ourselves euthanizing dogs that in the past might have gone to rescue,” said Katz, who created the plan with Dufty. “We give them a lot more time than any other shelter I know of in the state or country. Still, there comes a limit.”