MISSION, Texas—For many home buyers, the biggest motivations behind moving to a new neighborhood are a job change, rising wealth or a growing family. For Graciela Gonzalez, a private-school administrator from the nearby Mexican state of Tamaulipas, it was the constant threat of kidnapping and murder.

In 2010, Ms. Gonzalez said, eight parents of children at the private school where she works were kidnapped and held for ransom by drug-cartel thugs. Frightened they would be next,...