Well, in a democratic system, if the people vote someone out, they gotta go. But even that can get complicated when there's so many people out there making allegations about voter fraud and crooked elections. Theoretically, both sides may agree that the government should faithfully carry out the "will of the people," but nobody is ever really quite sure what the "will of the people" actually is at any given moment.
And even then, in practice, a lot of leaders don't seem to care much about what the people actually want, as much as they try to persuade people what they need or what they should want. Some might even develop a messianic complex where they decide that they know what's best for the people, even if they don't want it.