If you mean airbus FBW, AP OFF, side-stick left at neutral....
The FBW will try to maintain 1.0g in pitch. It has no pitch, speed or altitude targets to aim for, only load factor.
If Alpha exceeds Alpha Prot it will try to maintain Alpha Prot.
If the ATHR protection (Alpha Floor) engages as well, then the a/c will end up maintaining Alpha Prot with TOGA thrust.