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 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.)
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.
