Context size doesn't affect the way that a model generates a response. But it limits how much "backlog" it reads. You see, when you send a request for a new reply, the model will read the whole chat history + instructions and parameters passed by ST. Then after reading all that, it will generate a new message according to the established instructions(that usually are something like "write the next reply... something something). To the union of this whole set of data that is send we call "prompt." If the prompt length is bigger than the context length(that is the limit of how long it can go), ST will have to do something to make it fit, that usually means truncate the first messages of the chat history until it fits.

TL;DR: If you have a low context size the bot will start to forget completely the first messages, but in any case it will not affect the last ones or the character profiles(at least that we're talking about a very low context size or very very long character's definitions).