After Haman's genocidal edict was sent out to all the people of the Persian kingdom why was there not a mass exodus of Jews to parts of the world not under the dominion of Achashveirosh and his law?
The first decrees went out on Nissan 13 3404, and they were a forewarning to a destruction one year in advance.
The people's first response was to fast, as well as mourn, weep, wear sackcloth, ashes and lament (Ya'arot Devash), and this took place starting the next day, Nissan 14.
It lasted 3 days and from it Hashem accepted their teshuva (Megilla 12a). Immediately after this was complete, Haman was executed. Within a few months, the decree was officially reversed (Sivan 23) and a counter-decree was sent.
Therefore it is conceivable that nobody ran away because the whole thing was over very quickly. It wasn't "completely over" until Adar 13 3405, but the danger was effectively over and it was merely a concern that some people might go against the new orders and kill anyway. I doubt that was the kind of mortal danger that would compel people to run away, as the original decree might have been.
Also note that there is plenty in the sources that the Jews fully accepted that this decree was from heaven and not a mortal "happening". They would have realised that running away would have done no good in the face of a decree from heaven. Instead they focussed on teshuva, as mentioned.
In Mechilta D'Rashbi, it says:
אין לך כל אומה ומלכות שנשתעבדה בהן בישראל ולא שלטה מסוף העולם ועד סופו מפני כבודן של ישראל... במלכות מדי הוא אומר... ושם המלך אחשוורוש מס על הארץ ואיי הים
There is no nation or kingdom which enslaved Israel which didn't control the entire world, for the dignity of Israel... By the kingdom of Media it says... "And king Achashverosh placed a tax on the land and on the islands"
(A similar sentiment can be found in the gemara of megilla)
So we see that Achashverosh ruled the entire world. Of course, according to history, this isn't accurate. However, it's possible the meaning is that Achashverosh ruled over the known, or at least civilized, world. Either way, the meaning is pretty clear: the Jews had nowhere to go.
It's an interesting question.
The story of purim takes place 57 years after the destruction of the first beis hamikdash. Jerusalem was decimated and destroyed, even the effort to rebuild the beis hamikdash was halted, by haman and his sons, and signed off by King achashverosh, which seemingly shows that Achashverosh had influence even in jerusalem.
Practically, Achashverosh had dominion over majority of the known world, it doesn't seem like there was an actual place for the jews to flee to - which also shows the magnitude of the decree.