They can't change your window after you've already started in that window (you must be pre-notified).
They can't change a window to an earlier window unless it is the first day in a string of reserve days.

They change windows all the time, especially between long call/short call (that is contractually required). They can change short call windows to make a trip fit (no A3 reserves left, trip starts at 745am, so change an A4 to A3)