Not long after stuntpeople for Vin Diesel, Michelle Rodriguez and the rest of the “Furious 7” crew filmed their usual death-defying car chases on a twisty mountain road west of Colorado Springs, Colo., Richard Jansen received a call. Somebody from the movie had seen his “we buy junk cars” highway sign, and wondered if the owner of Bonnie’s Car Crushers could haul away 20 or 30 vehicles smashed beyond repair, including several black Mercedes-Benzes, a Ford Crown Victoria and a Mitsubishi Montero. “Sure,” Mr. Jansen said.

Then...