Well, suppose you have a gain 2 non-inverting setup. Vin+ > Vdd/2 means the op-amp cannot actually make the summing node Vin- anything like Vin+.
So Vdd=5, Vin+=5, Vin- = B.rail = 2.5: error is +2.5 - not a "working/normal" error voltage but an ERROR voltage (big time).
So the output hits the rails.
As Vin + gets higher, the error voltage Vin+ - Vin - rises from a normal "enough to drive the loop via AB" to something crazy lit 1, 2 or more volts.
OK: Now can I rig a feedback which essentially lies dormant until the error voltage exceeds maybe 50mV, then jumps in to force balance?
Yes - the output will not then be 'correct'. But it would be wrong anyway, and I at least the output is not at the rail.
