If a stable coin demand rise then the value and price will automatically rise and in this way it will get much attention in the market while to hold this kind of coin is a good way to sell at high price.
That wouldnt be a stable coin anymore lol. If the demand rises on the stable coin there should be more supply to maintain stability, if there is less demand then the issuer has the duty to buy every coin that is dumped.
I don't think the stable coin is ever present in a crypto market, unless it didn't enter any exchanges which impossible since how can it get high demand. It may vary on caps and how the team will handled it.