Mike Coffman, the conservative Republican mayor of Aurora, Colo., said he was at home on Tuesday night watching the presidential debate and bracing for the worst.

And then there it was again, before tens of millions of viewers: former President Donald J. Trump, describing Mr. Coffman’s Aurora, a sprawling suburb just east of Denver, as a city under siege, terrorized by migrants.

“They’re taking over buildings,” Mr. Trump said. “They’re going in violently.”

Mr. Coffman was contrite on Thursday as he told that story. After all, he had helped create the tall tale now sullying his city’s reputation.

Before Springfield, Ohio, before the misinformation about devoured pets and the memes of Mr. Trump rescuing ducks and kittens, there was Aurora, pop. 404,219, supposedly overrun by the violent Venezuelan street gang, Tren de Aragua. Those claims became a cause célèbre for the right-wing media, and ultimately a key focus of Mr. Trump’s anti-immigration repertoire as he escalated his attacks on immigrants as part of his campaign’s effort to capitalize on voter concerns about the southern border crisis.

Caught in the middle are a number of migrants, living in dilapidated apartments that Aurora officials now call squalor, amid “criminal elements,” not widespread gang activity, and unable to find or afford better. The buildings are nonetheless at the center of a national firestorm.