Magnetic field saturation in ac circuit
As inductance falls due to the saturation of the core, with a voltage source supplying the stimulus, the rate of change of current increases proportionately. Given that Faraday’s law of induction is: -

$$V = L\dfrac{di}{dt}$$

The induced voltage remains largely the same. This of course assumes that the voltage supply is capable of delivering the high current needed during core saturation.

This is quite commonly observed in transformers when the core is saturating quite badly; the secondary output waveform still looks nicely sinusoidal despite the current input to the primary being quite nasty looking.

Here is a good picture that is quite revealing. It shows a sine wave voltage across an inductor, the distorted current waveform and the magnetic flux as a result of core saturation: -



So, despite the core saturation, a decent sine wave shape is seen in the flux. Picture from here.