That's what research by a University of Illinois business school team found, when it collaborated with the Society for Human Resource Management to examine whether turnover was greater under good and bad bosses.

Essentially, they said, turnover's about the same. It's the buzz that the former employees carry with them into the marketplace that's framed by the former boss.

And that buzz can be very beneficial to a former employer, depending upon the value of what the researchers called the "LMX"—the leader-member exchange.

This all-powerful relationship is carried out into the business world with departing employees. A good LMX bodes well for the ex-employer. A bad one …. Well, not so good.

Read: What happens when nobody wants to be the boss?

"After leaving, whether or not ex-employees (i.e., alumni) harbor goodwill towards their former organizations is likely to depend on their LMX quality prior to leaving.

Alumni goodwill matters because organizations can potentially reap important strategic benefits from their alumni," the researchers wrote in an abstract of the article, which appeared in Personnel Psychology.

"We find that among employees who quit, pre-turnover LMX is positively related to higher salaries and greater responsibility in their next jobs, and is also positively related to alumni goodwill. Moreover, the strength of the LMX-alumni goodwill relationship depends on whether managers made robust retention efforts after employees communicated their decisions to quit."

Researcher Ravi S. Gajendran, a professor of business administration at Illinois, concluded that former employees "can potentially be important strategic assets in the future, provided they leave on good terms."

Drawing upon data retrieved in interviews with employees who had left jobs, he said: "If you have a good relationship with an employee who's left to join a client or competitor, you can leverage that relationship and potentially use them as a source of future business or as a back-channel source of information.  Therefore, thinking of ex-employees as a strategic constituency is something more organizations should start doing."