People aren’t trees. You can’t cut off a dying branch and watch it rot in the soil and expect that to be the end of it, because it isn’t.
People are different. The person you cut off might be dead to you, but they’re still alive and kicking in the minds of everyone else. You’ll still see their face on your social media feed, and people will still mention their names in passing even when just hearing the first syllable makes you cringe. It’s unavoidable unless you cut ties with every mutual friend you have and maybe move to another country. All you can do is just queasily scroll to the next post on Facebook or feign an enthusiastic smile and a nod, then quickly change the subject. People can’t know that you hold a grudge, an automated knife your ribs that triggers every time that one person’s presence, no matter how wispy, permeates the conversation in an offhand comment. If people knew you were “really that petty” then they’d cut you off, too, in which case — good luck to them because then they’d begin to know the exact same feeling.
I guess the proper response to these toxic feelings towards an individual would be to not hold a grudge, which in my opinion is the more harmful choice. Some might consider this calculative, to take note of every (major) wrongdoing dealt to you, but if someone hurts you and constantly does so, even when they know they’ve been hurting you (because you’ve talked to them about it) — why should this even continue? People forget that they come into our lives just as easily as they leave. Being friends for years really doesn’t mean anything if what they do in your friendship has started making you uneasy and/or sad, things like subtly taking advantage of your kindness or dismissing whatever negative emotions you’re feeling. You shouldn’t force yourself to remain somewhere that only aggravates you.
Forgive and forget? Maybe forgive, but never forget. After all, they forgot about you — and when they’ve forgotten about your feelings and welfare long enough, let them go, run as far away from as possible and never look back. If you see them around, say hi if you have to, or just dash unblinkingly and dramatically into the nearest sunset. You can leave, because people aren’t trees. They aren’t bound by roots.