This is for DH.
He is NC with an abusive parent for over a year, basically since not long after DC was born. He was LC for a few years before that. The parent has never met DC but nor had they expressed any desire to do so after they were born before DH went NC and other relatives, whilst they try and get DH to reconcile, have never said the parent has expressed any interest in seeing DC. They didn't pass on any gift when they were born, nor birthday card, nothing.
FWIW I don't have a strong opinion on this, don't think it is my place to really. I support DH whatever relationship or lack of he wants with this parent. I would never allow DC to be left with the parent unsupervised but that's my only red line on this and DH agrees with that anyway.
Oh, the parent has mental health problems and BPD btw. They are also now claiming a life limiting, possibly terminal illness but we don't actually believe that (they have form for previous similar lies).
We have always agreed that we would go to any family events they are at because why should we and DD miss out just because of them? However in practice obviously this is more difficult than a glib statement. DH has missed one event because he was too anxious about it with the parent being there (was evening event so I was going to stay home with DD anyway). He has another event coming up that we have decided me and DD also won't go to due to difficulty in us getting there (DH will be going straight from work). However before we discussed the travel logistics DH has been v stressed because on the one hand he wants us all to go to things and not miss out, especially DD and for his elderly relative who is dying to see DD and us, but on the other hand he finds it v stressful the thought of his parent meeting DC.
So really how do other people navigate these things?