Some people call it the Uncle Fred factor. A Transition CEO comes into a founder-based business only to find a close friend or member of the family - Uncle Fred. He may be a do-nothing freeloader or a know-it-all who stays on the payroll simply because no one can fire him. Usually his (or her) tenure is dependent entirely on the good will of the founder.
New CEOs who can't accept such a quirky practice will have a really difficult time operating in this kind of environment. Uncle Fred can't do much good, but he sure can do harm. The cycles the new CEO will spend trying to neutralize Uncle Fred or trying to rid the organization of their uncle, will be time that could have been spent more productively elsewhere.
I learned the hard way that Uncle Fred is often a cost of doing business. If you can just keep paying Fred and shuffle him out of the way, that may be fine. Otherwise, if he causes chaos, you may need to take more drastic action. Savvy board members, including venture capitalists (whom I would have thought would be too cheap for this practice), will often advise that Uncle Fred should be treated gently. His departure should be handled gracefully and sensitively, often paved with more than a few dollars and continuing benefits. This, I have found, is a very inexpensive way of dealing with a tricky issue.