Some say they were first brought in to take out the rats. Others contend they wandered in on their own.

What everyone can agree on — including those who have lived or worked at Chile’s largest prison the longest — is that the cats were here first.

Known simply as “the Pen,” the 180-year-old main penitentiary in Santiago, Chile’s capital, has long been known as a place where men live in cages and cats roam free. What is now more clearly understood is the positive effect of the prison’s roughly 300 cats on the 5,600 human residents.

The felines’ presence “has changed the inmates’ mood, has regulated their behavior and has strengthened their sense of responsibility with their duties, especially caring for animals,” said the prison’s warden, Col. Helen Leal González, who has two cats of her own at home, Reina and Dante, and a collection of cat figurines on her desk.

Prisoners informally adopt the cats, work together to care for them, share their food and beds and, in some cases, have built them little houses. In return, the cats provide something invaluable in a lockup notorious for overcrowding and squalid conditions: love, affection and acceptance.

“Sometimes you’ll be depressed and it’s like she senses that you’re a bit down,” said Reinaldo Rodriguez, 48, who is scheduled to be imprisoned until 2031 on a firearms conviction. “She comes and glues herself to you. She’ll touch her face to yours.”

Formal programs to connect prisoners and animals became more common in the late 1970s, and after consistently positive results, they have expanded across the world, including to Japan, the Netherlands and Brazil.

They have become particularly popular in the United States. In Arizona, prisoners train wild horses to patrol the U.S. border with Mexico. In Minnesota and Michigan, prisoners train dogs for the blind and deaf. And in Massachusetts, prisoners help care for wounded or sick wildlife, like hawks, coyotes and raccoons.

Connecting inmates and dogs has repeatedly been shown to lead to “a decrease in recidivism, improved empathy, improved social skills and a safer and more positive relationship between inmates and prison officials,” said Beatriz Villafaina-Domínguez, a researcher in Spain who reviewed 20 separate studies of such programs.

Dogs have been the most common animal used by prisons, followed by horses, and in most programs, animals are brought to the inmates, or vice versa. In Chile, however, the inmates developed an organic connection to the stray cats who live alongside them.

Yet there was a time when the relationship was not so positive. A decade ago, the cat population was expanding uncontrolled and many cats were getting sick, including developing a contagious infection that left some cats blind. The situation “even stressed out the inmates themselves,” said Carla Contreras Sandoval, a prison social worker with two cat tattoos.

So in 2016, prison officials finally allowed volunteers to come care for the cats. A Chilean organization called the Felinnos Foundation has since worked with Humane Society International to systematically collect all of the cats to treat, spay and neuter them. They have now reached nearly every one.

Like the inmates, the cats’ living conditions vary by section of the prison. During a recess period in one of the most crowded areas, where 250 prisoners share 26 cells, prisoners packed a narrow passageway, with clothes drying overhead and cats darting between their feet.

Eduardo Campos Torreblanca, who is serving three years for aggravated robbery, said each cell cared for at least one cat, but his kitten had recently died. “He was tiny, a baby,” he said. “And someone stepped on him.”

When the volunteers first arrived in 2016, they counted nearly 400 cats, a figure that left out newborn kittens and a large cat colony that mostly stuck to the roof. Now that number has been steadily declining. Why? Consider Mr. Nuñez, the home-burglary convict with two years left on his sentence. When he is freed, what would happen to his cat, Ugly? That was easy, he said. “She’s coming with me.”