Experimental studies have shown that low-pressure inductive discharges with attaching gases are subject to instabilities near the transition between capacitive (E) and inductive (H) modes. A global model, consisting of two particle and one energy balance equations, has been previously proposed to describe the instability mechanism. This model, which agrees qualitatively well with experimental observations, leaves significant quantitative differences. In this paper, the model is revisited with Cl₂ as the feedstock gas. A novel treatment of inductive power deposition is evaluated and chlorine chemistry is included. Old and new models are systematically compared. It is found that the alternative inductive coupling description slightly modifies the results. The effect of gas chemistry is even more pronounced. The instability window is smaller in pressure and larger in absorbed power, the frequency is higher and the amplitudes of oscillations are reduced. The feedstock gas is weakly dissociated (≈16%) and is the dominant positive ion, which is consistent with the moderate electron density during the instability cycle.