After a dude makes a Serendipitous Arrival, if a React causes them to change locations, do they automatically leave the shootout?
Shootout: Play a dude from your hand into your posse, reducing their cost by 5. When the shootout ends, pay 3 ghost rock or discard that dude.
Two such examples include F1 Burch and Stagecoach Office:
React: After F1 Burch enters play, move him to the in-town location of one of your other dudes. You may attach a non-Unique, non-Gadget goods from your hand or discard pile to one of your dudes at that location, reducing its cost by 1.
Controller React, Boot: When you bring a non-token dude into play, place that dude at any location you control.
I ask because I know there is precedent for participating in a shootout but being in a different (albeit adjacent) location, using Angélica Espinosa with or without her Buffalo Rifle:
Shootout: Angélica joins a posse at an adjacent location without moving or booting.
If this dude is adjacent to the location of a shootout or a job's mark, they can join a posse, without moving or booting, even if booted.
In short, if a dude arrives "into your posse" but changes locations without being "sent home booted", is it fight or flight?