The centre of pressure moves rearward after the critical AoA and after there is LESS lift, not no lift, this moves it further aft of the CoG which increases the moment between the two, aiding recovery. Very important with this to understand that it's RELATIVE airflow as well because you can stall inverted in a loop for example and the "nose down" actually becomes a reduction of elevator input or more correctly a reduction of the AoA.
There are quite a few different forces going on but as you would have seen the result of the AC wants to correct itself, and is the case in most examples with a few exceptions such as spiral dive.