Operational amplifier and negative feedback
In a properly operating amplifier, the sense of the negative feedback will be correct, even if the magnitude of the output is limited as in the diagram you show. The feedback will drive the circuit back to balance, and eventually, to roughly equal inputs.

However, there are some opamps, usually older rail to tail types, where the sign of the gain reverses when the inputs exceed their input common mode range Vcm. These types of amplifier can therefore 'lock-up' as the intended negative feedback becomes positive. I guess this wasn't seen as a fault to the original amplifier designers, as inputs outside Vcm are not 'allowed'. But it's such a common fault condition to occur that it's tripped up scores of amplifier users. 

It's now been fixed in newer opamps, that state proudly in their datasheets that the gain doesn't change sign, stays well-behaved, even when when the inputs are taken outside Vcm.