DALLAS — When a lost, stray or abandoned pet entered an American city’s animal shelter 10 years ago , there was a good chance it would not leave.

But in a quiet transformation , pet euthanasia rates have plummeted in big cities in recent years, falling more than 7 5 percent since 2009 . A r escue, an adoption or a return to an owner or community is now a far likelier outcome, a shift that experts say has happened nationwide.

The New York Times collected data from municipal shelters in the country’s largest 20 cities, including two in the Los Angeles metro area. Many of the shelters do not track outcomes uniformly or make historical data readily available online. Until recently, there has not been a concerted national effort to standardize and compile shelter records.