The market has always been following the rule of thumb, the law of supply and demand.
Nonetheless, the supply limit of any coin. The demand for it will still be the one that will declare and portray its price.
The variable that will become stable is the market activeness. Will this also lead to a stable monetary value of the coin?
The stability of the coin is being determined by the demand and you're right about the activeness of its market. If the market for that specific coin is very much active and has liquidity, we can say that it's stable in a manner of demand and liquidity. But to say that its value will become stable monetarily, it's a different side. We're talking about cryptocurrencies that have two kinds, the stable coins and the normal cryptocurrencies that have high volatility which most of them are.
And that's the basic part and structure of a cryptocurrency, being volatile.