I think firstly, you'd need to trust that they are genuine. Just because they say they are, doesn't mean they are.
Have they said this before and then gone back to previous behaviours?
And I don't think there is a direct link to holding onto pain and going no contact. You can let go pain whether you are or are not in contact with someone. It doesn't matter what the other person does or doesn't do: carrying pain or letting it go are things we do internally for ourselves.
So you can have all sorts of mixtures:
Parents go into recovery but you still carry around pain even though they are changed and you have a relationship with them.
Or, parents never change but you do a lot of work within yourself and you have worked through the pain.
Is there a particular reason you are asking this? Are you going through this at the moment?
You are wise to ask
2 reasons I ask
I was raised by 2 alcoholic parents
Lots of trauma for me from that as I felt lost and unheard and unseen a lot of my childhood
I live with my dad after mom passed
He hasn’t had a drink in decades BUT he’s dry not sober ( still is very anxious and drepressed which looking back probably drove him to drink)
When he gets like that I feel sympathy knowing he tried his best to parent and is definitely showing up for me now
Much better than bitterness I could feel
Secondly since I was I diagnosed CPTSD I raised my own 2 children with lots of hyper vigilance and dis regulated emotions
Married a man with CPTSD so my kids had it rough
No physical abuse but lots of emotional neglect looking back
My son used heroin to cope and passed in 2016
My daughter has decided her upbringing is the cause of her problems and is “taking a break” from me
Since I just recently got this diagnosis I have been addressing it
I am changing through therapy baby steps
And I am so extremely remorseful about pain I’ve caused
My beautiful son gone
My sweet daughter possibly gone as well