If someone commits a terrible crime and then flees to another country, are they free?

There’s always extradition.

I think they’re free in any country that doesn’t have an extradition treaty with the country the criminal is fleeing.

Many countries have mutual extradition treaties, meaning that criminal charges brought against a defendant can be pursued with the cooperation and consent of the new country’s police agencies, and the person can be arrested in the new country and bound for trial in the jurisdiction of the alleged crime.

But those aren’t universal, and even when they exist, sometimes the treaty is contravened by, for example, the intent of the prosecuting jurisdiction to seek a death penalty against the person, where the new country won’t normally permit that. So if the prosecuting jurisdiction agrees to waive the death penalty (take it off the table, that is) then the treaty can and will be enforced.

Like every other area of law, there are hoops to jump through and loopholes to escape through. And in some countries, even when the treaty exists, at least nominally, the law enforcement capability is lax (or incompetent, or simply bribed) to make prosecution a moot point. That’s pretty much what happened in Pakistan for Bin Laden to be able to live there for the past five years.

There’s a whole process for this called extradition. The problem is that foreign countries have no obligation under international law to hand over anyone within their domain. Many have agreements to do so, but those agreements can be limited. Countries without the death penalty, for instance, may refuse to hand over suspects without some assurance that the person will not be subject to execution.

Also, the authorities of one country have no right to pursue a criminal in another country without permission. So crossing the border can be an effective way to get the police off your tail for a short period of time. It’s not like the movies where crossing the bright line means you’re free, however; police will follow you over a border if they think they can get away with it.

As @weeveeship mentions, extradition is a possibility. However, it’s not always there, as @aprilsimnel. There must be an extradition treaty between the countries as well as one that covers the crime in question. Otherwise, extradition is a matter of discretion.

There is also the shadowy methods of rendition – which is the extrajudicial kidnapping and transfer of a person to another country for trial. That’s illegal in the international sense – but it happens of course.

Many countries, further, will refuse to extradite an individual to a country, even if there is an extradition treaty, if that country would inflict a punishment like the death penalty regardless of the crime. Abolition states refuse to do say because extradition, in essence, is the state acting to put a man to death,

Finally, there are classes of crimes that may be considered political, and therefore may result in a country acting essentially as an asylum nation for individuals within their borders. Certain violent crimes may have been done in the name of freedom from government tyranny (e.g., the difference between a terrorist and a freedom fighter), and the courts will often refuse to extradite for fear of supporting a governments persecution of its citizens.

If they can be extradited, then hell no, and don’t forget about bounty hunters or really pissed off intelligence agencies. Remember, Israel’s Mossad hunted down many former Nazi SS troops who hid in other countries and killed them.

It would depend upon the crime and whether they qualify for an Interpol listing.