In fallout (original) you could get 0 stats. Sort of.
Try to get a lot of radiation in Glow, than wash it away, and you still die on the way back - your stats keep dropping due to radiation delayed effect, and when one reaches 0, you die. I had to drug my char in most games just to keep SPECIAL above 0, to make it to the nearest town.
As for the way to kill in Barter Grounds - has anyone tried to enter with ticking explosives already on him? I can't find any, but it may be worth a try.