By the early 1890s, entrepreneur John J. Cain had established a facility for storing scenery from closed Broadway shows. The scenery was rented to stock companies and tours. The business operated successfully until 1938 when the steadily diminishing road forced its closure. During its nearly 50 years of operation, the phrase "going to Cain's" meant that the show in question was about to close.
The Historical Dictionary of the American Theater. James Fisher.