President Trump on Monday asserted that his Democratic rival, Joseph R. Biden Jr., wants to “destroy” the “American dream” by filling the suburbs with low-income housing projects.

The poster child for his bleak vision? Westchester County, N.Y., one of the wealthiest areas in the United States.

It was at least the third time in recent weeks that Mr. Trump had cited Westchester as a bellwether of his unfounded doomsday scenario that Democrats are bent on unleashing a torrent of violence and crime on America’s suburbs via housing policies meant to reduce segregation.

“Westchester was ground zero, OK, for what they were trying to do,” he said on Monday, in an interview on Fox News with Laura Ingraham, referring to Mr. Biden and his fellow Democrats. “They were trying to destroy the suburban, beautiful place. The American dream, really. They want low-income housing, and with that comes a lot of other problems, including crime.”

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Where does Westchester County fit in?

“I’ve been watching this for years in Westchester, coming from New York,” Mr. Trump said at the White House in July, promising to end the rule. And there certainly have been high-profile fair-housing fights in the county just to the north of New York City.

The best-known may be the federal segregation case that Yonkers fought for 27 years, as documented in the book and HBO series, “Show Me a Hero.” The city nearly wound up bankrupt before finally capitulating in 2007.

A broader case emerged in 2006, when the Anti-Discrimination Center used a novel approach to sue Westchester for failing to adequately address the fair housing issue in its overwhelmingly white villages and towns as required under the 1995 rule, while still collecting millions of dollars a year in federal aid.

Three years later, a federal judge ruled that the county had indeed misrepresented its desegregation efforts.

The county and the federal government subsequently entered into a consent decree that, among other things, called for Westchester to build or acquire 750 homes or apartments — 630 of which were to go in towns and villages where Black residents made up no more than 3 percent of the population and Hispanic residents less than 7 percent.

A housing official in the Obama administration, which approved the agreement, described it as “historic” and said it would allow the federal government “to hold people’s feet to the fire.” Six years later, the Affirmatively Furthering Fair Housing rule was introduced.

The 750 homes were eventually built, but Craig Gurian, the Anti-Discrimination Center’s executive director, said many were in areas that did little to truly integrate largely white communities.