All good things must come to an end. This includes your antagonist’s story arc. How it ends is often the most important part of the story, and it's something that you have to plan out in advance. Don’t write the rest of your story and then have no idea how to have your antagonist’s character arc end. This is important to do with any character, but it's especially important here, as the villain is one of the most important characters in the whole story, and often reflects the themes of your story.
The pure evil villain is almost impossible to redeem simply due to the fact that they are evil. Someone who has no strings attached, and is willing to deal all sorts of damage to everything around them, and is focused on achieving their goals at all costs to others is someone who usually can’t be convincingly redeemed. Usually the reason there’s a purely evil villain is if you want to focus on the heroic characters without giving them an opposite and if you’re okay with morals being somewhat black and white.
So what do you do with a purely evil villain? Having them deal with the consequences of their actions is pretty much your only option. Depending on your story and the world you’re telling it in, having them end up dead, or in jail, or lonely is likely your best choice, as it's often a way of showing that whatever immoral actions you’re trying to highlight will be punished. However, it is common to show that they’re ready to take another shot at their plan, although I would discourage doing this unless you already have plans for a sequel.
A sympathetic antagonist on the other hand is practically begging to be redeemed, although how you do this can be a point of conflict. Doctor Octavius in Spider-Man 2 redeemed himself but sacrificed himself to do so. However, it seems as if about half of Dragon Ball Z villains redeem themselves relatively easily. Again, this often comes down to the tone of your story. Something that’s more light-hearted can get away with an easier redemption, while if your story is more serious, the sympathetic villain often will have to die in order to redeem themselves.
Also, if your sympathetic villain survives, do they join your hero or do they go off on their own in some way. You might be tempted to keep a popular antagonist around, and that could very well be a good idea. However, when your cast gets too big, each character makes up a smaller and smaller role in the plot, making it harder for minor characters to become memorable. Now, I’m not saying you can’t keep new characters around, especially if older characters are rotating out, but this is definitely something to keep in mind.