> What circumstances are those?

If there is an act of war or natural disaster, the U.S. is good at extracting its citizens. There is also a decent precedent of negotiating to release people taken hostage or held prisoner by unfriendly regimes. (Or causing a fuss when Americans are harmed in a friendly country.) That, in turn, has a deterrent effect.

For Americans with access to legal counsel and the State Department, the benefits expand. Rich, overseas Americans thus present a unique free-rider problem.