“It runs hot and cold,” Inspector Kenny said. “Right now it’s spiking.”

The drop in auto theft has been a nationwide trend: Just over 721,000 vehicles were stolen nationwide in 2012, down from 1,246,646 a decade before, according to the National Insurance Crime Bureau, a nonprofit organization that tracks vehicle theft on behalf of insurance companies. Frank Scafidi, a spokesman for the organization, said it was not unusual for older cars to be targeted because they were easier to steal. But he had never heard of a scheme like the one in New York.

And it is catching the owners of older vehicles off guard.

Shirley Boyce of Bushwick, Brooklyn, said she stopped worrying about parking her 1985 Cadillac on her block long ago. She had no lock on the steering wheel and no alarm when it was stolen in November 2012. “The car was 27 years old,” she said.

At the time, Ms. Boyce thought that the thief might have appreciated the car’s vintage styling. “He was able to get it started with a knife or a screwdriver, you know, in the old-fashioned way,” she said.

Later, she learned, it had been scrapped for cash.

Ford Econoline vans, bare-bones cargo vehicles used by many businesses, have proven popular at scrap yards; they can weigh more than 5,000 pounds and fetch $600 to $700 for scrap.

“Anytime you see one of those on the scale, you got to look hard,” said Michael Downer, a manager at Atlantic Recycling, a Queens scrap yard. Nearby a worker slammed a pickax into the undercarriage of a Lincoln Town Car to drain it of gasoline.

“A big enough screwdriver and you’re in and out,” Mr. Downer said of the Ford vans. “That’s their favorite.”