@eskie as mentioned by the other member, some people can, others can't. I personally use to think I could, and wanted to in the past, but I can't. I use to think that because they're such a big part of my life and because I cared about them, that I wanted to stay connected somehow, still grow together but as friends or to delay the void or hold on to whatever is left.
However, regardless of you're reason the complications will still be there. Risk of backsliding, finding it harder to move on while they're around, getting feelings hurt if you see them with someone else or you get relegated in their priority list etc (you're just a friend now, you share that position with dozens of others now), future relationships can be impacted by them being around, or you spend too much time and emotional attention on them which could be given to someone else and after all of that... The relationship can still decay in a very short period of time, if their new partner doesn't like the idea of you two being friends, things will change VERY quickly.
The question you need to ask yourself is do you think it's worth it? Do the pro vs con and can you do it. Some can, others can't.
These days when faced with the dilemma, I say I need time for myself, and cut the person out fully in every way out of my life. Once an entire year has passed I revise the situation If I still want to be friends I do it, if not I leave it. You'll be amazed at what time and distance can reveal.