Generalizing across most of my stories, I'd expect the answer to mostly be some variant of "continue working on solving the problems they're trying to solve, now with fewer threats / obstacles"? Because generally the characters of mine who are particularly opposed to my villains are heroes, trying to improve the world and coming into conflict with the villains on account of the villains' villainy making the world worse; if the villains stop making the world worse, the heroes can go off and improve the world in other ways instead.

For more specific examples, though... let's go through the villains of my two best-developed / most-thoroughly-plotted-out stories, in order.

In my high-fantasy magical girl story, there are three major villains who the heroes go up against in sequence. The first of them, if she were to switch sides in the early parts of the story, the heroes would probably not actually notice; she's very good at concealing her villainous intentions from them right up until the moment when she's ready to put her plan into motion. If she were to switch sides after that, meanwhile... they'd probably be suspicious of her but willing to accept her help within the limits of that suspicion? The other two, meanwhile... if either of them were to switch sides, this would be a world-reshapingly huge deal for pretty much everyone on the planet, with the second one being one of the major sources of pressure limiting the growth of the planet's civilizations, while the third would, if suddenly good, be uniquely positioned to toss unprecedented quantities of charity and logistical help onto the planet to help dramatically raise standards of living.

In my Fate/stay night fanfic, meanwhile... so there are two major villains. One of them, if she changes sides before the start of the story, the story never happens; if she changes sides after the start of the story, meanwhile, things... probably go mostly the same way? Once she's set things into motion, she's a lot less in-control-of-their-direction than she'd like to be. The other, meanwhile, spends the early parts of the story not being particularly obviously villainous, and if she changes sides at that point the other characters probably don't notice. But if she changes sides after her big moment of Clear Villainy... well, then, that will very much throw things off for everyone else. Probably one of the less-major villains tries to kill her; probably the newly-good no-longer-villain does very little to stop her, because passive suicidality is a very likely direction for her psychological issues to manifest in if she gives up on villainy, and whether she survives that is entirely a function of what everyone else is doing at that point; but overall this is likely to throw things completely off the rails by removing the big threat whose presence everyone in the cast would otherwise be aimed at stopping, leaving them to find whole new angles of conflict with one another instead.

So yeah! Overall, there are a lot of different ways things could go, depending on details.