NEW YORK — Time may be running out for the horse carriages that carry tourists around Central Park. Mayor Bill de Blasio already has declared his intention to shut down the industry, saying it is inhumane to keep horses in modern-day Manhattan.

While that debate could be over, at least one nagging question remains: What will become of the horses?

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Both sides in the carriage horse fight insist they will find a sanctuary for the approximately 200 horses licensed to pull carriages in New York City. But drivers warn that shutting down the city stables might have the unintended effect of eliminating a rare outlet for surplus horses pouring out of the farming and racing industries — sending them faster to the slaughterhouse.

“If they did not come to New York City, most of these horses would be dead,” said Ian McKeever, an Irishman who owns nine Central Park horses and has been driving a carriage in the city since 1987.

That’s an argument that infuriates the loudest critics of the industry, who say the nation’s unwanted horse dilemma is no excuse to preserve an inhumane business.

“Anyone who cares about a horse wouldn’t think that taking it and sticking it in midtown traffic is the right answer to that problem,” said Allie Feldman, executive director of a leading anti-carriage lobbying group, New Yorkers for Clean, Livable and Safe Streets.

Last year, roughly 140,000 U.S. horses were shipped off to slaughterhouses in Canada and Mexico when they became unaffordable, or unprofitable, for their owners.

The root of the problem is unregulated breeding, said Wayne Pacelle, president of the Humane Society of the United States. Every year, far more horses are produced than can possibly get lifetime, or even middle-aged, care. The number of sanctuaries for retired horses is small — only around 500 nationwide.

In Pennsylvania’s Amish country, which is the source of many of the horses that wind up working in Central Park, this oversupply plays out weekly at the New Holland Livestock Auction. Every Monday, buyers for foreign meat factories snap up horses — many still young and healthy — that once pulled plows, buggies and carts, or even served as family pets. All have been discarded because of lackluster performance or rising costs of care.

McKeever cited the case of his oldest horse, Roger, who was neglected and malnourished when he bought him from a Pennsylvania farmer in 1999. Roger is set to finally retire this month to a preserve on Long Island, McKeever said, after 15 years on the job in Central Park.

Another of his horses, Danny Boy, won trotting races in Australia and the U.S. before suffering a tendon problem. He, too, was headed for slaughter before getting a second chance as a carriage horse.

“When you give a horse a job, he is protected,” McKeever said.

Carriage opponents note that, for a lot of horses, New York City is far from a permanent home.

City records on 720 carriage horses registered in the city from 2005 to 2013 show that about 30 percent spent two years or less on the job, according to an analysis prepared by the Coalition to Ban Horse-Drawn Carriages.

Industry critics say that turnover represents large numbers of horses who are given a brief tryout in New York but don’t last because they can’t acclimate to the job or urban life.

The city does not track what happens to horses that leave the business.

Carriage owners insist their horses are as healthy and happy as any in a well-run rural barn.

Most live in one of four stables, hidden away inside old three-to-four-story buildings on Manhattan’s far West Side. On days they work, the horses clop through city traffic, amid honking cabs, for up to 2 miles before reaching the spots where they line up for customers near Central Park. Most of the rides are in the park itself, but during some hours, the horses are allowed to visit a handful of other nearby attractions, such as Rockefeller Center.

Mishaps involving horses that bolt or get hit by cars make headlines every few years, with the most recent traffic or spooking deaths in 2006 and 2007.

“Horses do not belong in the middle of traffic in New York City. They do not belong in an urban environment like this. It’s not safe for them. It’s not fair when you think about what their lives should be and what our society is like,” de Blasio said last week during an appearance on Comedy Central’s “The Daily Show.” He has favored replacing the hansom cabs with old-timey electric cars.

At the largest of the city’s barns, Clinton Park Stables, the horses have enough room to lie down on beds of straw. They get regular visits from veterinarians and horse dentists. The building is equipped with sprinklers in case of fire. Overall, the horses appear to be in fine shape.

But there are drawbacks. The stables have no outdoor areas, so the horses must spend all of each day either in their stalls or in harness on the street.

Every horse spends a minimum of five weeks each year at an out-of-town farm, but critics say that isn’t enough for animals that would benefit from daily turnout in a pasture.

Douglass Newbold, a dispatcher at the Large Animal Protection Society, a volunteer organization that enforces anti-cruelty laws in Pennsylvania, said horses clearly weren’t meant for city living, but life in the countryside is often just as grim.

“If you asked the horses, ‘Do you want to be out in a mud paddock with no feed, standing in a snowstorm, or in a dark stall on the fourth floor of some building in New York City?’, I’m not sure how’d they’d answer.”