What happens after a widespread social chaos?

It very much depends. Post-Soviet economies after 1989 had less social turmoil and crime, but experienced much more severe economic crises. If people are willing to give democracy a try and there is foreign assistance (esp. in economics), there is a good chance of success. The most important thing is to preserve order. Once you slide into chaos (riots, rampant crime, destruction of property, terrorist attacks) it's very hard to fix the system.

After the Mazdak revolution in Persia in 6th cent(with slogan: slaves, ground and women must belong to everybody), the population was practically annihilated, so Arabians came almost to an empty place later.
After the 184–204 riot in China there remained about 7 out of 50 millions of population.

After French revolutions of 1789–1871 the France became a country much more convenient to the simple people. And as for victims, there were not more than tens of thousands of them – incomparable to about 7 millions of the Russian revolution (with civil war), for example.

According to the theory of ethnogenesis of Gumilev, ethnicities have several kinds of turmoils.

1. Turmoil at the start of a new sound ethnicity – in this case, the near future (100–200 years) is very violent – life is too creative for a normal being (in the terms of contemporary Europe), but most of the people are not normal, so it is OK for them.

2. At the apex of an ethnicity's existence (War of red and white roses in England) – after it the even and creative centuries of civilization stage come, changing much later to the stagnation stage.

3. At the end of the ethnic existence – the stage of obscuration comes – very long total moral degradation that longs until all resources created by previous stages are consumed.

4. Start of a new ethnicity with a defective base idea (communism, mazdakizm, yellow sky of justice), about 10–80 years of utmost cruelty and degeneration. The annihilation of the previous ethnos is a sure thing – only biological heritage remains. Morals are absent). This variant is the worst of all, similar to 1+3 mixed together.

5. During the civilization phase it is difficult to provide the necessary structural changes, but people sometimes need them. So, lesser revolutions come. (French revolutions) I think the Egypt revolution is of that sort. But you should make these necessary system changes you need. Or else yet another revolt shall come, and another… And after all those, you won't have active people. And the 3rd variant will come.

This could go anywhere.

The French revolution:

Started with the overthrow tyrannous rule and ended with the beheading of many people, a failed republic, and many years of turmoil. France was surrounded by many sates, and so, was at war a lot, impoverishing people everywhere. In France, the revolution wasn't good for the people

American Revolution:

This revolution was a revolution against the government breaking the laws. It started off with years of war, then turmoil because the Federal Government had no power, then became a world super power. It should be noted that America was isolationist, and so, didn't go to war too often.

Egypt:

The revolution started off against tyranny. The rebels were divided. Some were secretly hoping for power, others were sincere in trying to liberate Egyptians from tyranny. Today, the military runs the government, and it might go the way of America, or the way of south America(below).

South America:

These revolutions started off against colonial rule. Like Egypt, some rebels had good intentions like Simon Bolivar, but others, just wanted power. These revolutions ended up creating all powerful governments.

Chinese Revolution (#1 in 1911)

The revolution was against a corrupt rule and succeeded. The revolutionaries were united by Sun Yat Sen, and changed China into a republic. Unfortunately, there were evil people who took advantage of the system and became dictators. China stayed poor.

I'd say that Tunisia is quite a bit like Egypt right now. Though it probably will not become a super power, it could stabilize, but it could also just end up with all powerful government.

I'd also like to add that sometimes, an authoritarian rule isn't always bad. Take for example, Singapore, it is a nanny state, and controls the lives of its people, yet, it is doing quite well. Also take China as an example. If the first revolution was a failure, then the second, using communism, was successful. Today, China isn't a Stalinist state anymore, but an emerging super power.

What happens after "widespread social chaos" is difficult to predict as it often depends on local conditions combined with regional and international considerations. There are often two requirements that a nation needs to fulfill after any internal disorder, those being economic sufficiency and a need to establish a system of just governance. In many cases, particularly after very violent confrontations, people trade the elements of the latter requirement for the former and promote the rule of a strong leader. This is particularly evident in the French revolution where the near-genocidal reign of terror lead many of the French towards supporting Napoleon, a leader who though despotic was both sympathetic to the revolutionary goals and brought military and economic success to the country. The former has particular importance as the revolutionary goals encompassed in the saying of "fraternity, equality, and liberty" were the social motivation that lead to the revolution. Napoleon would have been incapable of mustering such widespread support without appeasing the social/economic grievances of the French proletariat.

Tunisia's case is difficult for the reasons stated by Omar in addition to regional and international elements. While Tunisia is more economically advanced than most of its neighbors, it certainly does not have the massive oil wealth boasted by some of the Arabian states, the cultural influence of Egypt (mostly Cairo specifically), or the military power (and unwavering American support) of Israel. Thus while the "strongman solution" is likely given the current internal factors of Tunisia, it is also very unlikely due to the relative regional insignificance that Tunisia will be able to recover via economic or military conquest (like France in the aforementioned analogy).

I am not particularly knowledgeable on Tunisia, but from what I do know it does seem that the Tunisian revolution was largely successful. Many of the political demands seems to have been met (even if in a limited fashion). The more corrupt and autocratic elements of the government likely realize that American support is too tepid to be of assistance and that reliance on the EU economy will mean allowing more political freedom. Given this, I doubt that Tunisia will devolve into the state it was prior to the revolution in the near future, but like I mentioned before, the temptation of having a "strong leader" will be ever present. With the advancements in establishing a "system of just governance", the importance now will be in economic development. If the economic expectations of a large number of Tunisians becomes more likely to be unfulfilled, it is then quite likely that a sufficiently charismatic leader could install themselves and roll back advancements made in political freedom.

You are describing a chaotic situation. Almost by definition, how things develop out of a chaotic situation cannot be predicted.

For what tiny bit it's worth, here are a few things I think history (both old and recent) can tell us.

• When you finally let everyone have their say (vote), rather than just the activated people in the streets, you are likely find they are surprisingly reactionary. (See recent elections in Egypt and Iraq, the Second French Republic)
• If things get bad enough (sounds like they are there now) and someone comes along who somehow credibly promises and end to the chaos, the public are likely to embrace him no matter what his politics. This is typically how democracies die.
• (related) The next time things come to a free and fair vote, whoever is in charge during a downturn as bad as you describe will almost certainly be voted out, no matter whose fault the situation really is or how odious the opposition is.
• If your society is corrupt (eg: bribery is a way of life), it really doesn't matter much what form of government you have. If you want things to get better, the way people relate to each other and the government has to change.
• If things eventually do get reformed as a result of this, there will (quite rightly) be statues and monuments to Mohamed Bouazizi all over the Middle East.

Everything hinges on good people keeping engaged and not letting the sacrifices that others already laid down for them go in vain.

But you are there, on the ground, with at least some small ability to influence what will happen. So really we should be asking you.