Since cloud droplets form on aerosols, such a decrease leads to low concentrations of droplets also, which results in larger droplets on average.
Larger droplets produce drizzle more efficiently.
A drizzle-dried air parcel in a downdraft will evaporate all its water before reaching the average cloud base. Because it is not energetically favorable to push a warm parcel downwards, complete boundary layer mixing is inhibited. Yet another mechanism contributing to the breakup is the evaporation of drizzle below cloud base. Again, this potential energy is released through cumulus convection. An additional factor is the role of entrainment of the warm, dry air above the boundary layer, but this is only a slight modulator in the simulations we have performed so far.