Their population is increasing so much that many deem the cats a public health nuisance, for both humans and other pets. They can carry fleas, parasites, and deadly diseases, such as rabies. And they're at the mercy of weather, animal attacks, vehicles, cruel people.
These elusive cats are difficult to count. But nationwide, some experts put the free-roaming population at about 80 million - equal to the owned cat population.
"The issue constitutes a national tragedy of epidemic proportions," said Sheilah A. Robertson, an animal welfare expert with the American Veterinary Medical Association.
In Philadelphia, "a lot of people aren't aware of the free-roaming cat population," said Angela Messer, director of operations for the Pennsylvania SPCA, which has launched a new spay and neuter program.
"They don't understand there are colonies of upwards of 40 cats that are living out there with no one responsible for them except for a handful of really dedicated people."
These people, like Cureton, provide minimal care and shelter, if no more.
Cureton, who lives in a rowhouse in the city's Hartranft section, started feeding strays when one of her pet cats ate poison and died. Although struggling financially, Cureton spends more than $80 a month just on their food.
Philadelphia and the broader region also have numerous shelters that take in cats and try to find homes for them - and that spay and neuter cats, tens of thousands a year.
And still the cats keep coming. There's not enough room. Or money.
"It's a needle in a haystack compared to what is needed," said Kathy Jordan, a financial planner who heads the Philadelphia Community Cats Council, a nonprofit.
She's also one of the city's best-known trappers - a little-known group, expert at trapping free-roaming cats and getting them care, including spaying and neutering.
She's never without traps in her car - a bumper sticker reads "my favorite breed is rescued."
Jordan knows where most of the colonies are, but won't say, partly because "it's easier to tell you where one isn't."
Also, Jordan has seen what happens when a site becomes known: People drop off unwanted cats, upsetting the fragile stability of a group of cats. Fights occur. Worse, if the new cat is a female that hasn't been spayed, the colony begins to grow.
But many colonies exist near parks and waterways. One well-known colony is near the Walmart along the Delaware River.
There were always feral cats. But their number exploded after cats eclipsed dogs in popularity in the 1980s and few efforts were made to neuter them.
The math of cat fertility is impressive. A cat can have her first litter at six months of age. She is pregnant for about two months, nurses for another two, and then can start again.
Various groups have done "cat pyramids," showing all the progeny one cat and her kittens can produce. Spay USA, an advocacy group, shows that in just two years, one cat can become 67 cats. In five years, 11,801.
"You can't stop the cats," Jordan said.
In a room full of cages, an empty one is merely temporary. One cat has left; another is likely on the way.
"You are looking beautiful, yes, you are," Sue Cosby coos to King, who is next to Magnificat, upstairs from Sonia. Every incoming cat that doesn't have a name gets one.
Cosby is executive director of the Animal Care & Control Team of Philadelphia, which has a $3.9 million city animal control contract.
Typically, the facility on West Hunting Park Avenue in North Philadelphia takes in 20,000 cats a year, plus 10,000 dogs and 2,500 other animals. In summer - kitten season - they can get more than 100 cats a day.
"It's overwhelming," Cosby said.
Studies have shown that if everyone looking for a pet cat got one at a shelter rather than at a pet store or similar place, Cosby said, the shelters would soon empty.
But that's not happening.
Cosby has begun to view feral cats as a kind of hybrid, neither pets nor wildlife. "They're part of the environment now," she said.
Most want to see the adoptable cats taken off the street and put in homes, but debate rages over what to do about the rest - the wild, unfriendly feral cats. Most think their numbers should be reduced. But how to do it effectively and humanely?
Cat advocates claim rounding them up and killing them is not only cruel, but also useless. In what they call the "vacuum effect," other cats will simply fill the void.
Recent efforts have focused on a technique called trap, neuter, and release, or TNR, championed in this country by a Washington, D.C., group called Alley Cat Allies.
Founder and president Becky Robinson said the idea is to stop the breeding but let the cats live. In time, the colony will decline.
"Rounding up and systematically killing millions and millions of cats . . . doesn't match the moral ethic of our communities," she said.
A group of cats under the Atlantic City Boardwalk is often cited as a success story.
About 12 years ago, 250 cats were living there. Public health officials teamed up with Alley Cat Allies. Within a year, homes were found for more than 60 kittens, and all the adults were fixed.
Now, said Robinson, "there's no reproduction. The cats are living out their lives."
The ASPCA, the Humane Society of the U.S., and the American Association of Feline Practitioners have all endorsed TNR.
One of the most vocal opponents has been the nonprofit American Bird Conservancy, which objects to outdoor cats because they kill birds.
Recently, scientists from the University of Georgia and the National Geographic Society fitted small cameras, dubbed KittyCams, around the necks of 60 house cats allowed to roam outdoors.
The researchers concluded that nearly one-third killed animals - an average of one for every 17 hours a cat was outside, or 2.1 a week.
Conservancy spokesman Robert Johns derided TNR efforts, renaming them "trap, neuter, and re-abandon."
When the neutered cats are put back in their colonies, "everyone rejoices that they saved the cats," he said. But, "they have just put a very effective, very efficient predator back in the wild."
In one towel-covered prep area, an anesthetized Twilight gets an ID collar and his genital area is shaved. A vet checks his heart and gives Twilight a distemper vaccine and pain medication.
Slit, squeeze, snip. Ten minutes later, he's done.
In another area, Leigh, a little black female, is being strapped onto a spaying board. She'll be prepped on it, go into surgery on it, and, 20 minutes later, come back out on it.
The Pennsylvania SPCA has pioneered advances in spaying and neutering, taking almost an assembly-line approach. The idea is to reduce the time so they can spay and neuter more cats.
The facility on Erie Avenue in North Philadelphia, considered one of the nation's most progressive, does the surgeries seven days a week, and the staff can handle about 60 to 70 cats a day.
Recently, the SPCA launched a Free Roaming Cat Program that offers streamlined processing and reduced prices for regular trappers like Jordan.
Before the program even officially began, in July, more than 30 had registered.
For an extra $10, a trapper can surrender a friendly cat for adoption; the agency does not euthanize except for medical reasons.
To head surgery vet Adam Corbett, caring for cats is all part of a continuum.
"As long as we're going to have cats in our homes and treat them as pets, we can't ignore the cats that are out on the street. It's a fluid population" that often interacts, he said. "By addressing the free-roaming population, we help every cat."
Neutering is now considered to be so important that medical advances have taken place. A female cat can now be spayed when she's two months old - as opposed to six - or two pounds. A $25 million prize has been offered to the entity that develops a sterilization injection that can be used in the field.
As Cureton continued to call, more cats came.
They were especially cautious this time because one of Kathy Jordan's cages was in the path to the food.
Some had blunt right-ear tips - good news. It's a nationwide sign that the animal has been spayed or neutered.
Jordan would target, instead, a cat that had a large wound on its back.
She suspected cruelty. She sees it all the time - cats dead from drinking antifreeze, cats burned from firecrackers tied to their tails.
"You want to see the bad side of people? You've got it here," she said.
Ever so slowly, the black cat crept closer. "Come on, Precious," Cureton cooed. "Nobody going to hurt you."
One step more, and the cage banged shut.
That night, a veterinarian examined the cat, concluded a dog had bitten it, and performed surgery.
Contact Sandy Bauers at 215-854-5147, email@example.com, or follow on Twitter @sbauers. Read her blog, "GreenSpace," at www.philly.com/greenspace.