For example, Mr K was on holiday overseas (in a foreign country). He got into trouble and got arrested or asked to appear in court in that country. He decided to leave that country and come to Australia thinking he would be safe here or he may have a legitimate reason to leave the country other than just trying to avoid getting arrested. What happens to him?
Australia has a treaty or agreement with many foreign countries which requires Australia to provide support to the foreign country to bring offenders to justice. That means if the foreign country sends a request to Australia with the information that Mr K has an arrest warrant against him, Federal Police can arrest Mr K in Australia and later extradite him to the requesting country. Australia also an Act to extradite a person.
Papazoglou v Republic of the Philippines  FCA 254 is a good example which sets out the laws, regulations and agreements relevant to such scenarios.
“It is to be noted that s.3(a) (of Extradition Act) contemplates that a person (including an Australian citizen) may be extradited from Australia without the need for the extraditing country to provide evidence of guilt. Curiously, most treaties applicable to non-Commonwealth countries require no evidence of guilt to be produced by the requesting party, whereas the scheme applicable to Commonwealth countries requires that a prima facie case be established.”
It means that the requesting country may not need to prove that you are guilty to have you back in that country.
At the same time, it is not straightforward that just having an arrest warrant in a foreign country means the person can be extradited to that country. There are a lot of processes that must be followed for such an event to happen. A magistrate may have to make a decision and the Attorney General makes the final decision.
In short, if you have an arrest warrant in a foreign or overseas country, do you not take the matter lightly or try to overlook thinking it might go away? In almost all countries, you fail to appear in court, an arrest warrant usually gets issued. If you have to leave that country, make proper arrangements with a criminal lawyer in that country before leaving and follow their advice. It would cost you a lot more if you make a wrong decision in such a scenario.
It is not always the case a person leaving a country has an arrest warrant to avoid justice or to flee from getting arrested. There are many reasons, such as requiring to have proper medical treatment or fear of unknown territory or not understanding the law. If you need help, feel free to contact me or a Criminal Lawyer in Brisbane who has the experience of such matters.