Death Equals Redemption

Often, when a character who has done something bad or evil sees the error of their ways and does a Heel–Face Turn in the course of fighting to undo the damage, their redemption comes at the cost of their own life.

There are any number of reasons that authors do this:

1. It shows that the ex-villain is serious about helping the heroes, enough to risk death to save them. It also plays up the drama of having a character turn good, but then tragically not survive to live out their redemption. This version is sometimes subverted with Redemption Earns Life or Redemption Equals Affliction, especially if the ex-villain is popular enough; since the willingness to die is all that is needed in this version of the trope.
2. It may be that the bad guy is just so bad that it's hard to accept the idea that they get a happy ending even if they've sincerely changed their ways, and so they have to die to make things seem right. Sometimes Executive Meddling forces this so as not to cross Moral Guardians who will object if the ex-villain suffers another suitable punishment. See Do Not Do This Cool Thing.
3. Maybe the author is reluctant to change the status quo of the story by introducing an Anti-Hero to the cast but still wants an antagonist to be sympathetic, so they have the villain redeem themselves before dying. Thus the main cast experience What a Senseless Waste of Human Life.
4. It could be that there is no place in the world for them. Sure, the redeemed villain going off to a happy little life with Babies Ever After is heartwarming, but it might just not be possible if they're especially infamous with the general public. Even if the heroes are willing to forgive the ex-villain it doesn't always mean that the Muggles will comply. In this case death by Heroic Sacrifice may actually be a happier end for the character than being strung up by an angry mob. If subverted the character may end up having to hide their identity or go into exile otherwise the heroes may end up having to plead the villain's case.