The output state of this circuit is not determined by its inputs. Let's trim away the two input gates with constant output (the AND and the NOT) and just consider the ones involved in the feedback loop. The lowermost input to the AND gate is 1. The lowermost input to the OR gate is 0. We name the output X, and can set up the following equation:
X = (X OR 0) AND 1
Indeed, the second AND gate can also be removed, as AND 1 is redundant:
X = X OR 0
The OR gate can also be removed, as OR 0 is also redundant:
X = X
This tells us nothing about X. In other words, X is free, and the output will be stable whether X starts at 0 or 1.
In real life, X is neither 0 nor 1 when the circuit is powered up, but the physical implementation of logical gates favors 0 and 1. Therefore, any initial, induced or spontaneous imbalance will quickly lead to one of the two stable states.
A different scenario arises when there is no self-consistent X, such as for an inverter (a NOT gate) fed back on itself:
X = NOT X
This is self-contradictory and leads to oscillations in digital logic circuits. If NOT(X) were a physical implementation of 1-X, there would be a valid fixed point at X=0.5 *, but again, digital logic circuits strongly favors the high and low states.
* Corresponding to a truth value of 0.5 for "This sentence is false.".