So, there's a villain. Right. Murdering, world-conquering type. The series is ending, so it's time to get rid of him. Slowly and painfully. So he goes out with... a final touching quote and a One-Woman Wail?
As odd as it may seem, if you want the audience to feel sorry for a villain, a good death scene is probably the way to go. This works best if you know their Freudian Excuse; Chaotic Stupid need not apply for this sort of thing. Also works easier if this is a supporting villain. This is easiest to do with a Big Bad's minions: we can identify with The Dragon, and especially the Quirky Miniboss Squad, over time and may be sad to see them go. If a Fallen Hero or a Tragic Monster dies, expect everyone to weep openly. A few well-chosen Last Words may also be used to create this feeling.
Note that if you want the audience to take the scene seriously then you have to add some humanizing elements to your villain beforehand. See Likable Villain for ways in which this can be done. Neglecting to do this may result in Narm or just confuse the audience.
A Woobie, Destroyer of Worlds, a Tragic Monster and other kinds of Tragic Villain are the best choices, but any case of a genuinely well-done Anti-Villain will do. Also note that this is primarily about the story showing how sad a villain's life was, not how some of the audience will interpret it.
Compare Draco in Leather Pants, Cry for the Devil, What a Senseless Waste of Human Life, Antagonist in Mourning, and Death Equals Redemption. Do not confuse with Alas, Poor Scrappy (though it can overlap), and share the Super-Trope of Dying Moment of Awesome. Or Alas, Poor Yorick for that matter. Contrast Asshole Victim villains, who are so deplorable that their death elicits no sympathy — although some clever writers have found ways to overlap the two.
Villains who are Complete Monsters can never qualify for this trope. As said villains are completely unsympathetic and aren't meant to be mourned in any capacity. In the few instances where the hero and/or audience does sympathize with a CM, it's for the most part to establish how heroic the protagonist is.
As a Death Trope, several if not all Spoilers will be unmarked ahead. Beware.
