I worked an SPT show where the Equity ASM left the show permanently for MRE as an Actor in a production at another theater (he was actually taking over for an actor who had to leave that show). As I remember it, the outgoing-ASM was training the take-over ASM during the first part of Tech Week, and the take-over was running the show for all or most of Previews.
The transition went smoothly, in part because the PSMs of both productions were friends, so there was good communication about where the outgoing ASM would be on a given day, and our production was given priority since we were opening sooner. Also the incoming-ASM had worked under our PSM before, so there was as little anxiety as possible about how The New Kid would fare. Even though it seemed like everyone understood the ASMs motivation for leaving, and weren’t personally angry, it unavoidably added stress to the production process. I’m not sure how the producers felt about the situation, as far as whether they would be willing to hire ASM 1 again.