Lets simplify this to one phase and pure resistive loss in the power line. Let's assume the power company hasn't line protectors which trip at certain current.
If we assume the power company outputs voltage Uo to a rural village but there's resistance R in the supplying line which causes the actual voltage in the village be Uv=Uo-IR where I=the total loading current of the village.
If everybody has a voltage stabilizer and everybody have ON certain devices which need certain total power P one can calculate What is the remaining Uv.
Substituting I=P/Uv one gets a 2nd degree equation for Uv. It has a solution if P is equal or less than (Uo^2)/(4R). In that case there's still Uv at least Uo/2 and everybody are happy except the power company who dissipates substantially power in the wire resistance. The limit case is when the dissipation in the wire resistance is as much as the power consumption of the village. That's the maximum available power to the village.
If the inhabitants demand higher power than (Uo^2)/(4R) there's no solution, the current increases, the voltage drops and finally the stabilizers stop. The voltage can be back until the stabilizers start again want too much.
Assuming pure resistance is nonsense. There's transformers and the lines itself also have capacitance and inductance. Voltage stabilizers which take more current when the voltage drops can be considered as negative resistance. The whole circuit has good chances to be an oscillator which works with the same idea as a microwave diode oscillator (=negative resistance diode in a reactive circuit). Another unreal assumption was the lack of protection devices in the distribution system. The power company cannot allow too high dissipation in their devices, so a part of the load will be dropped off.