Are M15 & M16 different geometry such that one has a slightly lower Vgs but lower gm so that there is a neutral point of uA current swing at some middle of the range of Vc input. Thus creating offset above and below this point? just a guess.
I think C1 and C2 are short for AC signal so circuit working normally.
But when there is an offset in VGA probably because of high gain output voltages will be 0 and VDD. (Vo+ =0 and Vo-=VDD if Vcm1 = Vcm2 +Voff )
This time M13 is on and M14 is off so M13 adds more current to that branch (M2 branch) and compensate this unbalance so again Vo+ and Vo- meats somewhere Vo+ = Vo- = VoDC
Won't talk about transistor being "on" or "off", the circuit should work in linear range normally. It's simply a negative feedback path with low pass characteristic.