My final words were in an email about a month ago. It was after a really difficult period where we were kind of still in touch (well basically I kept calling her to beg her back, not dignified at all but this was my first real break-up lol...) I'd got very angry with her about her new bf who she'd started seeing only about 2 weeks after we split up; and I suddenly felt incredibly remorseful, I think I was still in the not-allowing-myself-to-be-angry stage. So I sent a longish email basically absolving her of any blame, saying I'd definitely like to be friends somewhere down the road once I was over her, etc. Basically absolutely everything she would have wanted to hear. This was written at a time when all I wanted was for her to 'forgive' me for being angry with her, altho I now think she probably deserved a bit of anger frankly.
I knew it was going to be my last bit of contact - she sent a reply which I could have replied to but didn't see the point in which she said 'take care' etc. and that the fact I'd 'believed' her over the new man meant a lot, which it probably did (I'd thought she'd cheated but actually I really don't think she had, but she still moved on far too quickly IMO). None of this was terribly dignified for me. BUT - what I realised is, I'd got into a position where I could never leave things perfectly, with everything said exactly how I wanted; in any case, I'm still going thro emotions now, every day I think of some little thing I could have asked her, sorted out, etc. The fact is I pushed her enough to know that she left me because she no longer loved me (all her other reasons were excuses to protect me, but I'm definitely the type that HAS to know) and nothing else beyond that really matters - I just need to focus on me now.
The main motivation for going over 'final conversations' etc. in the dumpee's mind is to look for chinks of hope, or wonder if you've 'left the door open'. Well it was in my case anyway; and all that is destructive. The door needs to be closed firmly, and moving on should be the order of the day. That's not to say that anyone on this thread who's thinking of breaking up shouldn't think carefully about 'that last conversation'...but if it's over it's over, and dwelling on final bits of contact, while inevitable, is best avoided.