Cost Down vs. Skull Lair

A monster is always at least 1 Star. And Cost Down only affects monsters in your hand so it would have no effect on Thousand Eyes regardless.

So to give an example that actually works. If you have DNA Transplant active changing all monsters to Water, and A Legendary Ocean on the Field reducing all Water monsters by 1 Star, your Thousand Eyes Restrict would still be a 1 Star monster.

Or if you equip Demotion to your Mega Thunderball he becomes a 1 Star Monster.
 
What anthony said also applies to Atk and Def, a monster cannot have less that 0 Atk or Def.

Just though it was good to know ;)
 
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