There are many places that do not extradite, even if you are known to be living there.

Life on the run is a Hollywood thing - the CIA isn't going to kick down her door and blackbag her back to the US. If she leaves the US, she is effectively gone unless she does something really stupid.

The CIA does not deal with fugitives....but the FBI does. They have a task force devoted to tracking down fugitives.

The FBI generally works through Interpol to bring back international fugitives (for example, Tamara Dadyan) but will also "blackbag" fugitives if necessary. It's just not necessary to do that very often.

The list of countries that do not extradite or cooperate with international law enforcement is surprisingly large... it's not just tropical islands.

There's also plenty of countries that would enjoy harboring a wanted US person.

The list of countries that don't extradite to the U.S. and the list of countries a wealthy person would want to live in don't have much overlap, unless you think Syria and Somalia are wonderful places to live. (There are a number of countries, like Indonesia and Vatican City that don't have extradition treaties with the U.S. but which will extradite to the U.S. through Interpol.)

Have you actually been to those places? Many of them aren't that bad, especially if you have money.

I lived for a period of time in Syria (Rojava). Spent most of my time fighting in the civil war (YPG), but also saw a bit of the civil side. Town like Qamislo (Kurdish controlled) are actually quite nice if you have a bit of coin. Fairly tolerant, lots of trade, tasty kebab and other restaurants, basic utilities including internet/phone, people are nice and accepting of varying religions and ideas etc. A couple hundred dollars a month would fetch an ok flat and plenty enough to eat. A few hundred more would hire armed guards and a couple hundred more your own driver. Syria is better than a cell by a longshot, and I've been in both.

And that's not including stuff like some of the federal court cases I've read from the Argentinian courts. Where they've granted people citizenship even after entering the country with fake documents and a criminal record. Sure someone like Elizabeth would get got, but you should really look into the number of annual extraditions and the kind of people that get taken. They're mostly high profile or violent criminals, the rest slip away or just run out of money or something like that.

The most famous recent example if probably Ghosn fleeing Japan to Lebanon. It does make one wonder how likely it will be for the next case. That being said, the coincidence of great wealth and being from a country that treats you as a hero and doesn't have extradition treaties with the west does seem quite low, but obviously not zero.