The Play As for StS clarifies how it is supposed to work.
Play As: Place on selected human Evil Character. Disease that character and decrease character 2/2 per turn. If character reaches */0 or less, convert character to a green brigade Hero and reset abilities (*/*) to face value. If converted, holder must place Sowing the Seed on another human Evil Character in territory. Effect is ongoing.
Line bolded for reference.
Thus:
1) There are two possible scenarios that I see. Either he is discarded like all other characters when they reach */0, and StS is discarded as well (since no conversion happened it cannot be transferred, and thus follows the host) or he is returned to face value, and then starts decreasing again. The reason the second scenario is possible is it is feasible to assume the "do as much as you can" principle applies here to the bolded line, that when the */0 condition is triggered, you try to convert but can't, then you try to reset and can, so the reset happens. Since nothing else happens to StS, it would continue working indefinitely. It is possible that the conversion and the reset are dependent on each other, i.e. they are so called "paired abilities" (a new REG term I believe) but I don't know enough about how they work to say for sure.
2) If he is protected from conversion and discard, and we assume the first scenario from question 1, then we introduce two more possible scenarios:
2a: The Hero decreases indefinitely to negative abilities.
2b: The Hero decreases to */0 and resets, then continues decreasing again.
This again depends on how the bolded line is interpreted. If you are not allowed to reset without conversion, then we get 2a. If you are allowed to reset without conversion, we get 2b.
Confused yet? Me too. This card is a pain for ruling questions.
I'll try to simplify:
Assume Conversion is not allowed
Assume Discard is allowed (question 1)
If Reset is not allowed, then we get 1a: Character and StS are discarded.
If Reset is allowed, then we get 1b: Character decreases to */0, goes back to face value, then starts decreasing again in an indefinite cycle.
Now assume Discard is not allowed (question 2)
If Reset is not allowed, then we get 2a: Character decreases to negative values indefinitely
If Reset is allowed, then we get 2b: Same as 1b.
Like I said, I am a bit fuzzy on paired abilities, and how to determine whether two abilities are paired. My intuition would say that for both scenarios, option b is the answer.