If you look at the history of the world and times of unrest, especially those that resulted in revolution, you can see a common theme of the hopelessness felt by the lower classes in those societies. This is particularly evident in the periods preceding both the French Revolution in 1789 and the Russian Revolution in 1917. The first action that the wealthy could have taken to mitigate unrest would have been to provide decently paying jobs so that people had a way to support themselves. In pre-revolutionary France, the rich ate whatever they wanted, and the poor starved. When people work hard and cannot provide for their families, hopelessness follows, and this breeds unrest. Even today, in our society, the growth of disparity between the rich and the not-rich is causing unrest. Many in our current society believe that the middle class and their way of life is threatened, and this is causing cultural strife. Thucydides recognized an important fact in his History of the Peloponnesian War, when he pointed out that "However well off a man is in his private life, he will still be involved in the general ruin if his country is destroyed." Many French and Russian nobles learned this fact the hard way after their country was destroyed and their fortune lost.
Another action the wealthy can take to help to mitigate social unrest is to work with governments to give those who are unhappy a venue in which to air their grievances and then to work with rather than against those with a grievance to resolve issues and problems rather than to deny them. The wealthy often have a powerful voice in government, and if they use that voice to solve problems rather than deny them, much unrest could be avoided.
Finally, the wealthy can also use their power to support the free choice of individuals as far as religion and cultural values go within the limits of a civilization. Being forced to go against one's conscience in the personal realm, as well as giving one religion too much power in the public realm, can cause unrest. That can be seen throughout history in the conflicts between Catholics and Protestants, and in many countries today as we grapple with multiple religions and value systems under the same legal system.
The biggest thing the wealthy have to be able to do to mitigate social unrest is to be able to put themselves in the shoes of those who are unhappy so they can understand their problems. Problems can never be solved without understanding.