As most historians can tell us, there are no absolutely stable societies. The most prosperous ones are doomed to sink into oblivion. However, what we are interested in most of the time is the transient stability that societies display. After all human beings only live a finite amount of time. The notion of society itself is much of a human construct: without the dynamical interaction with its constituent members, a society is merely a label that we impose on a group of people. And within such networks of interaction, we do see that the most extreme behavior usually incur the greatest threat to the sustainability of the society. If a society handles such internal stress well, then it is stable by definition.
On the most naive level, the legal systems provide societies with the most preliminary stablizer. If criminals were not tried in a court and punished according to some predrafted rules, any civilization will go down immediately as a result of unscrupulous actions of even just a few exceptional moral outcasts. Above the criminal laws come about civil laws, which literally brings the whole nature of legality onto a higher civic level. In a modernized society like ours, civil laws play a much more quotidian role than criminal laws, since it deals with more sensitive issues characteristic of social relationships between individuals. Such relationship could be family-oriented, or monetary. In the later case, since capital is the driving force behind the evolution of most societies, we see a clear need for its regulation. The recent event of south east asia financial crisis reminds us of how important it is for societies to incorporate measures against sudden change in its economic status, and to have competent financial advisory board to forestall such catastropic events.
Taking a different perspective, we see that another age-worn institution rooted from the most nascent societies in history, namely religions, also produce the same stabilizing effect on societies. The most quintessential example is probably Christianity. Since its advent, the European nations have enjoyed a relatively peaceful period known as the middle age. And the fundamental mechanism behind its pacifying effect is its teaching against violence and other types of extreme behaviors quite common in a period of rapid political power overturn. Another less well known example is provided by the Confucius teaching in Ancient China. It is an amazing poltical fate for ancient china to boast such long period of relative peace, deliminated by its dynasties which typically last around 300 hundred years. The essential ingredient in the Confucius doctrines is again civic comport and actions, but rather than with the promise of earning the ticket to heaven, the emperors made it a requirement for its office candidates to pass exams based on such teachings. The result of course was the same. While the merit system was able to select some of the best minds amongst its citizenry, it also set up a general tone of pacification and conformity in the geographically extended and multicultural nation.
Finally modern bureacratic politics also sought after social stability by employing such ad hoc devices as military suppression and political propaganda, often mixed together in a fussilade against certain extreme groups in the society. The recent attack on the western world by certain terrorist groups fueled the need for a regenerative security platform aimed at stifling further aggressions. The reaction is perfectly natural since it is the governments responsibility to help promote a sense of safety among its subjects. And the leaders well recognize that such critical moments in the history of their nation are the most indicative of their political leadership and stability of their nation. Therefore they usually become much more proactive and alert in such periods. In the United States, the president usually enjoys a brief rally period of high performance rating during national crisis, which for instance helped Franklin Roosevelt win his 4 straight elections. Such spectacular phenomenon also shows that the average educated citizens are very much aware of the need of a strong leader to fight against any imminent threat to social stability, and they do their best to promote the needed strength within their present leaders, by temporily relinquishing their true political and ideological beliefs.
Thus we have established a strong liaison between societal stability on one hand, and its defensive mechanism against internal radicals on the other hand. History has taught us over and over that a well-functioning society must be responsive and effective to deal with abnormal and devious behavior characteristic of us free-thinking human beings. Negligence of this essential duty will often result in the collapse of a seemingly invincible nation-state, such as the Roman empire, and inflict tremendous discommode among its citizens, which ultimately could lead to the termination of a political power.