See my root-level comment about potentially different behaviour and semantics for neurodivergent :).
For example, suppose you're at a party, talking in depth about a football team's season and they say something unrelated like "Oh by the way have you seen John?". It is usually a polite way to try to wrap up a conversation. A polite response would be something that graciously gives them permission to change the subject or leave, for example, "I think I saw him outside, maybe go take a look?".
Sometimes it takes the form of bored body language and sentences that don't lead the conversation onwards, e.g. "Yeah that's crazy" or "Well, what can you do...". In that scenario I like to give the conversation a respectable death, e.g. "Well, all we can do is hope for a better season in 2027!".
Some cues include the person physically squaring up to you front to front instead of being at an angle to you. Another cue could be touching you on the shoulder or forearm. For me the most obvious tell is that they are laughing or giggling.
Breaking rapport means the other person wants to disengage without offending you. I usually make the excuse I need to take a breather.
later, when going out with friends, if i ask "where should we go to talk", and you suggest someplace obviously loud and not great for conversation, this could be seen as a mild form of misunderstanding something i communicated previously about a personal preference in a given situation: breaking rapport
I suspect most people desperately trying to hang on to it, except with those they are good friends with. Unless they want out of a conversation. Although i may be projecting here.