What happens when you have your line resistance too high or your power supply voltage too low is a regulator current and voltage run away condition.
The regulator will draw more current, the line resistance will drop more voltage. Lower voltage on the regulator will cause it to draw more current and so forth until the regulator shorts out at theoretically infinite current and zero volts. Be fun to watch it on the bench. I presume it will be like looking at a crowbar folding.
