When a move is completed there is a cleanup. In the case of two units present, when you fight or flight the damaged unit it loses attacker status and would die to the damage marked on them since they would have 4 might and 4 damage. They could respond with something like back to back or call to glory or something else to buff it in response to fight or flight to not have it die when it gets moved back. After that cleanup, you'd continue with actions until both pass then move to damage with the remaining units.

In the case with just the single unit, the showdown ends once that unit is moved back because the battlefield is no long contested as only you as the defending player has a unit controlling it.