I've been on both sides of the old flame equation.
I split up with a long term partner about ten years ago and we remained very good friends afterwards. There was never any thought of getting back together on either side and the friendship turned into a more brother/sister type relationship
, which was great. We didn't live in the same town, so we saw each other a few times a year like any old friends might and caught up on the phone occasionally. Then a few months ago he got himself a new serious girlfriend and decided we couldn't be friends any more and after twenty years of knowing the guy, he cut me straight off and I haven't heard from him since.
On the other hand, a guy who I had a very short relationship
with about 8 years ago recently found me on FB. It was nice to catch up with him and lovely to exchange a few emails but then he started getting creepy and telling me he was still in love with me (dude, it was only three months to begin with!) and just wouldn't let it lie, so I had to cut him off because he made me so uncomfortable.
So I guess it depends on the people involved; there certainly isn't always the expectation or hope of getting back together, but that doesn't necessarily mean that just showing up would be a good idea. Guy 1, I'd have been happy to have show up at my door at any point. Guy 2, I would have been bolting the door and hiding behind the sofa