In the most cases, the source of the horrendous odour is some kind of decay within the lungs. This is evidenced by the fact that the odour always peaks immediately following the victim's coughs.
I have a theory that in some cases, the rot comes from smoking marijuana from a bowl that lacks a screen. Stems and seeds, when lodged in the lung, can create an environment for persistent bacterial infection. There is documentation somewhere of a girl who inhaled a seed that stayed in her lungs for years. Her notoriously bad breath cleared up after she finally coughed up the seed.