Those phrases often imply that they were fired or asked to resign - although the deniability can be useful, which is why they’re so often used. As a recent example, Fidji Simo went on leave from her role at OpenAI several months before leaving. Although I don’t know for sure, I would suppose that she was essentially fired when she went on leave, and the subsequent success of Codex after she went on leave confirmed the decision to fire her. It’s possible that, if Codex hadn’t been a success, she might have been brought back, so putting her on leave was useful for optionality.