In an article found by Jody’s crew, Forbes contributor Jack Zenger posits just that. He speaks of when he was a VP of Human Resources where there was a dictatorial VP of Administration whose subordinates were fearful of him and complained about him, but turned out to adopt some of his poor qualities as well. When he was terminated, the hope was that they would do well under new leadership but they did not and were ultimately terminated as well.
In the article he goes on to site some studies conducted between “alpha” leaders and their direct reports, “beta” leaders. Then looking at the engagement of the leaders to each other of the top 10% and bottom 10% in comparison, the lower percentile of alpha leaders had much, much lower engagement with their beta leader. This further impacted the next level down (below the the beta leader) as well in the same way.