It is a voltage follower with a transistor booster. Since the transistor is inverting, the normal feedback inputs to the opamp have to be swapped. It is only conditionally stable (or not) because the loop gain of combination is higher than the originally internally-compensated opamp.
The simplistic circuit you posted does oscillate in simulation. Look at the first circuit below. Once perturbed, it never stabilizes. The degree of oscillation depends on the Gain-Band-width Product of the Opamp and the gain/band-width of the transistor. It is worse with slower opamps.
A practical circuit requires some additional compensation, as shown in the second sim.