What happens when circulating supply reaches max supply?

Excuse me, could you elaborate on what precisely occurs when the circulating supply of a cryptocurrency reaches its maximum supply? Does this signify a halt in the generation of new coins, and if so, how does this affect the overall market dynamics and potential for appreciation or depreciation in value? Additionally, are there any precedents or historical instances where this scenario has played out, and how did they influence the trajectory of those particular cryptocurrencies?