It heavily depends on the tone of the campaign and the players’ preferences. Some groups, in some games, enjoy death being a potential outcome, while others prefer for it to be completely out of the question.

There are also many degrees between both, like how much should potential death be telegraphed before making a decision that could end on it, or whether it should be relegated purely to an outcome of bad decisions and never caused by bad luck with dice.

My personal favourite is for players to make a decision when they are defeated: accept death (or retirement) and have their sacrifice improve the situation, or be left at the mercy of fate and have to face other consequences (easily worse than a heroic death, if the players care about the story and the world).

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I think the best piece of advice I’ve seen about that particular situation, is to see what the player says (the exact words, tone, etc they use) as what their character wants to say, or what they are saying in their mind, but then the roll determines what is happening in reality.

Maybe your discourse that you were insecure about actually stroke a nerve and performs unexpectedly well at convincing the target. Or maybe what you think is the perfect speech is falling completely flat because the tone is way off, or you are sluttering, or you are too close or too far from the other person in an upsetting way. Just like in real life: who hasn’t had a joke we find hilarious in our mind be met with an uncomfortable silence and a quick change of topic? although that might be just me.

What I find it usually works best as a GM is to look at how the player describes their dialogue and if it’s something outstanding, or something absurd, adjust the difficulty (slightly, so the stats stay the most important factor) accordingly. It’s actually the same thing I would do when the players describe a battle tactic during combat, so it’s not exclusive to social encounters.