I would absolutely allow an enemy to deal subdual to the PC when he drops him below 0. To be honest though, I'm not certain as to whether or not the PC gets to make death saves (with the idea being that a 20 wakes him up). Certainly, the PC in question is not dying which would lend support to the argument that he not be allowed to make the save. At the same time, just sitting there with nothing to do, or even the chance to do something, would really suck for the player in question. I wouldn't apply any penalties for failing the saves though.
I guess the easiest thing might be to point to the rules for stabilizing a dying character. IIRC, stabilizing the character means he no longer needs to make death saves until he takes more damage. Now ordinarily, the character in question wouldn't want to take the save anyway since the chance of something positive (5%) is far outweighed by the chance for a negative (45%). But I think it would be reasonable to rule a PC who was knocked below 0 with subdual damage to be unconscious but stabilized. As far as I know, there's nothing official that allows the character to make a death save in this situation other than perhaps a succesful heal check by another PC.