How to demodulate an overmodulated signal?
This signal is half way between regular AM modulation (for broadcasting music) and full double-sideband-suppressed-carrier. Because there is still carrier present you can filter this out to give a constant amplitude sine wave at only the carrier frequency. Use this sine wave and the original "over-modulated" signal and feed them into a balanced modulator (aka 4-quadrant multiplier) to recover the base-band audio.