I think it just depends on a few things, #1, the kind of person you are, #2 the relationship you had before the break up, if they were friends or something.
I know someone who still keeps in touch with damn near all the men she use to date, and for whatever reason, remains friends with them. She hates to burn bridges, even if the relationship is over
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For me, when it's over, it's over. If I see ya, I keep walking.