The is a story told by Ben Bradley, which was used in the movie, "All the President's Men." Bradley tells about being a young political reporter and he gets a hot tip from a very reliable source. President Lyndon Johnson was going to replace J. Edgar Hoover, as Director of the FBI. Bradley started making calls to try and get confirmation, but no one would talk. The next day, LBJ has a ceremony in the Oval Office, where J. Edgar Hoover's appointment as Director became "for life."
Bradley's tip was real and Johnson was trying to push out Hoover, but trying to confirm the story tipped off Hoover, who was able to marshal his supporters and block LBJ's move. Bradley's editor supposedly said, "Congratulations, Ben. You got us stuck with Hoover, forever."
The politics of replacing a cabinet secretary or other high official are complicated at the best times, and if the secretary intends to hang on, it's very complicated. Heaven only knows why Sessions and Tillerson even wanted the job in the first place, much less why they would want to keep it, after finding out what it's like to be employed by Donald Trump.
Sometimes, the very act of reporting that someone is on the way out, is enough to keep them on the job. This must be some kind of Heisenberg Principle, applied to politics.