Back in 2014, not even Sting could rescue his Broadway show, “The Last Ship.” As the box office numbers dipped, he stepped into the production, hoping his fans would flock to the theater to see him onstage. But his time was limited because of a scheduled tour, so when that gambit fell short, the show was forced to close after 105 performances, costing its producers $15 million. And yet “The Last Ship” has refused to sink.