For most, it simply lapses without renewal. Moving is a bit of a wrinkle. I suspect, if you simply don't use your license after the move, you are fine, but you should call the ATF to verify.
That's for FFL businesses.
For collectors:
https://www.atf.gov/firearms/qa/are-licensed-collectors-required-turn-their-acquisition-and-disposition-records-atf-if