I think you might be getting confused with previous editions of DnD. In 5th edition, characters can never drop below 0 HP, and the concept of negative hit points for PCs does not exist. When your character takes damage that exceeds their HP or while they are unconscious, they are subject to the rules of either Instant Death or Damage at 0 Hit Points:
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum (PHB pg. 197).
Damage at 0 Hit Points
When you take any damage while you have 0 hit points, you suffer a death saving throw failure. If the damage is from a critical hit, you suffer two failures instead. If the damage equals or exceeds your hit point maximum, you suffer instant death (PHB pg. 197).
In conclusion - since a character can never have less than 0 hit points, you would never have to use Spare the Dying on someone with less than 0 hit points.