Dumbledore said to Harry, when explaining Horcruxes and souls, that killing split a soul in half. I took that to mean that there would be a half a soul floating around with no vessel. A true Horcrux is different in that one kills intentionally with a plan to create a Horcrux and carefully chooses the vessel it resides in,like the ring or diadem. A soul fragment from a random killing would probably just remain a useless fragment floating around, as there was no intent to kill to create a Horcrux and preserve it in a vessel, an act of unspeakable evil.

Dumbledore was trying to save Draco from damaging his soul by carrying out his plan to kill Dumbledore. He wasn't creating a Horcrux, but just the act of intentional killing would have damaged/split his soul. Severus then asked him, "What of my soul?" To which Dumbledore replied, "His (Draco's) soul is not yet damaged." (Meaning Draco had not yet killed anyone intentionally and Severus had. Dumbledore was telling Snape that his soul was already damaged from killing and killing again would not be as tragic as it would if Draco damaged his still innocent soul. No Horcruxes were being created though.