What happens when you get sued for civil matters such as breaching employment contract in one country, after you have already left to another country for good? What is the general protocol for these kind of cases?
In the absence of an agreement to the contrary, you could usually be sued in the jurisdictions where the events giving rise to the claim took place, if you were personally served with process anywhere in the world in a procedurally correct manner. If this happens and you default or fail to cooperate in the judicial process, you will probably have a judgment entered against you.
If you lost, the other party would get a judgment against you (an official declaration of a court that you owe another party money that authorizes various involuntary means of debt collection from your income and assets). This could be enforced against assets you have in the jurisdiction where the judgment was entered, or could be "domesticated" to a different jurisdiction where you had assets by bringing suit or exercising another process set forth by treaty or a law of the jurisdiction in which the foreign judgment holder seeks to domesticate the judgment.
Whether the foreign judgment is conclusive against you or not, depends upon the domestic law of the place where they seek to enforce the foreign judgment, the nature of the underlying claims upon which the foreign judgment is based, and the legal process used to obtain the foreign judgment.
Many countries will pretty much automatically enforce a judgment enforcing a breach of a contract between private sector parties obtained through the ordinary legal process in a country whose legal system is recognized by the U.S., but often will not give legal effect to legal procedures like a pre-dispute "confessions of judgment", an award of exemplary damages, an award of non-economic damages, or an award based upon a legal theory that is not recognized by the jurisdiction in which you seek to enforce the judgment.
In general, judgments of U.S. courts in tort cases are rarely recognized by other countries.
Similarly, a U.S. court, for example, would not enforce a foreign judgment, from say, ISIL controlled territory, for breach of a contract to deliver slaves to a buyer. Some Saudi Arabian money judgments are not enforced in the U.S. because the courts have held that their system does not protect basic principles of due process and the rule of law, which is why contracts with Saudi Arabia often have arbitration clauses instead of relying upon the royal courts in existence there.
Some countries might enforce a judgment entered following a trial on the merits regarding a dispute, but not a default judgment, without essentially bringing the lawsuit all over again in the country where the assets are located, applying the general principles of legal concepts known as "collateral estoppel" and "res judicata".
Most countries have special laws specifically governing when an arbitration award will be enforced with a money judgment in that jurisdiction and when it will not be enforced. This varies considerably from one country to another. The U.S. is unusually deferential to employment and consumer arbitration, but most countries will recognize express signed contractual arbitration agreements in a business to business situation that conforms to basic standards of due process.