This is how I see hp:
hp∈ℤ (that is: hp is an integer. {..., -3, -2, -1, 0, 1, 2, 3, ...}), but with a maximum value of your max hp.
hp≤-10 --> dead
-10<hp≤0 --> unconscious
hp<0 --> Awake
By this system, if I had 15 hp and was hit for 30 damage, my hp would drop to -15. Since -15≤-10, I am dead.
If my friendly neighbourhood cleric casts close wounds, his spell must put my hp>-10 to prevent my death. Close wounds effectively happens before the damage though, (from what I read anyway, since it "effectively prevents the damage") thus using it in arguments on how HP works will give nothing.
I don't have any RAW wording to support my idea of how hp works, this is just how I have understood the system. It is fully possible I have added logic which was not there when I heard the rules. Hope it helps though.
Best Regards
Yirrare