This is an edge case, but if someone:

1. Creates a Flow board
2. Posts some stuff to it.
3. Changes it to a wikitext page (has to be done manually)
4. Moves the wikitext page (and thus also the Flow board in its history)

BoardMover should still run so e.g. contributions show accurately, the null edit to update the header for the title is made (will only be evident if it's reverted back to being a Flow board), etc.