We don't currently have a concept of "inactive conversations" in Thunderbird. We have conversations that aren't currently joined but decided not to support that in the Matrix implementation for now to keep it simpler. However, leaving a room while keeping the TB representation open is unrelated to closing a conversation.
However "closing" a conversation has the same result with all protocols, you leave the conversation and the conversation is removed from the UI. We are aware that this user interface doesn't really match up with other modern chat client semantics and it's something we'd like to address eventually.