When Erika Lee wrote the Facebook post, it was just another summer day in Springfield, Ohio.

It was before the city got dragged into the presidential race, before former President Donald J. Trump stoked debunked rumors that Haitian immigrants were abducting and eating household pets, and before an ensuing wave of bomb threats upended life in the town of about 60,000.

Ms. Lee had heard that a neighbor’s cat had disappeared and that one of their Haitian neighbors might have taken the animal, so she posted the rumor on Facebook. But then she decided to go back to her neighbor.

“I asked her for proof,” Ms. Lee said.

It turned out the cat that had supposedly gone missing wasn’t the cat of a neighbor’s daughter, as Ms. Lee had posted. And if there were such a cat, it belonged to a friend of a friend of the neighbor’s daughter, Ms. Lee learned.

“And at that point, we are playing the game of telephone,” said Ms. Lee, who said she had no information herself about any abducted cats.

She has since deleted the post, but it had taken on a life of its own — eventually finding its way into the right-wing echo chamber, where it was picked up by Mr. Trump’s running mate, JD Vance, who grew up in Middletown, about 40 miles from Springfield.

Then, last week, during the presidential debate with Vice President Kamala Harris, Mr. Trump repeated the rumor, using it to drag Springfield into the national debate over immigration. “In Springfield, they’re eating the dogs,” he said. “The people that came in. They’re eating the cats. They’re eating — they’re eating the pets of the people that live there.”

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