When a conversation on a Facebook thread is most definitely over because you, or the other participant liked a comment rather than writing a reply. It can be due to the fact that the conversation has come to a natural end, or because a comment or request was made that could never be fulfilled or bettered.
Last week I was talking to an old friend on Facebook, I wrote on her wall, she commented back. It was all going great, so I thought I'd ask her if she wanted to go for a drink sometime. I knew it was never going to happen when she terminally liked my request.