Indeed. In the case I'm most familiar with, a whole lot of people decamped from impossible D.C. to Prince George's county, Maryland.
Now, to someone who lived in Arlington, Virginia for a dozen years the crime in PG was awful. To someone living in D.C. I strongly suspect PG was not bad at all, and being allowed to own a firearm in your house made I'm sure a significant difference.
Or take Boston, which the WASPs kept small after the Irish took over the city; without looking in more detail, the top level Wikipedia page indicates annexations stopped after 1874 with one non-WASP exception (https://en.wikipedia.org/wiki/Hyde_Park,_Boston).