Read some basics before asking, please.
PLL systems are very important in generating accurate and stable frequency, also in synthesizers. A phase or frequency-modulated signal can be well demodulated by a PLL system which recovers a carrier.
Locking characteristic is a very important feature in PLL system.
A PLL oscillator locked to a reference harmonic offers a very low phase noise defined by that reference.
Synchronised demodulation is required for accurate phase demodulation. if the local oscillator becomes "unlocked" then you will have a sinewave sitting on your output signal that is the frequency offset. Some sorts of AM using SSB/VSB, also need synchronous demodulation.
Frank