I remember hearing about a historical case involving a king (I think of England) that mentioned in passing that he would be happy if a particular person was killed, after which a knight hoping to gain his favour killed the person, sparking a debate over whether the king was responsible for the killing. However, I can't remember who the king was so I can't look up the case to learn more about it. Does anyone know what I'm talking about and who the king was?
Sounds like Henry II: "will no one rid me of this troublesome priest?!" The priest in question being Thomas Becket, Archbishop of Canterbury. Four knights went to Canterbury and assassinated him at the altar. Henry ended up doing public penance for it.
You are probably thinking of Thomas Becket, Archbishop of Canterbury, and Henry II, King of England. The phrase most commonly reported, even though of disputed historical accuracy, is "Will no one rid me of this turbulent [or meddlesome] priest?", which is probably way more direct than what Henry II actually said. Finding instances of the aforementioned quote is a trivial task, where it originated, exactly, I cannot say, though. A more probable version of the quote, "What miserable drones and traitors have I nourished and brought up in my household, who let their lord be treated with such shameful contempt by a low-born cleric?", is given in Simon Schama's "A History of Britain": https://www.book-info.com/isbn/0-563-38497-2.htm .
I hope this answer is in accordance with the subreddit rules, since I cannot think of what sources to cite, in this case.