In D&D, the rule was that if you hit 0 or negative hit points you were considered dead. Some optional rules also came out, which I partially adopted. I've always played OD&D in a similar manner of how the somewhat new C&C is run now, and I've been playing for nearly 25 years.
If you hit 0 or negative hit points I roll a d20 and check it against your constitution, with the negatives being a penalty against the roll. If the constitution check is made, then the character is conscious and the bleeding has stopped but the character shouldn't exert themselves (such as running, leaping, attacks, etc). If the check is not made than the character is bleeding and losing a hit point per round until they reach negative their max hit points or constitution score (whichever is higher). In which case they are dead. If they score a 20, they are instantly dead. If they score a 1, they can attack and cast spells.
I wag rules on occasion, so the above are the basics of how I handle the situation. When I checked Lola's constitution check when she went to -1, the result was a critical success... a 1. So I ruled she could attack and was otherwise conscious. If she tried to exert herself in a run I may have decided to make another check for consciousness.