One more vote for a minimum of 1 on either.
Side story: in 1e, I watched my best friend roll up a PC with the stats 18, 17, 16, 16, 14, 4. It was that last 4 that was the killer. He put it in Con, and his elven wizard suddenly had a lot in common with Elric. 1-2 hp max per level caused him to...