This trope is not as common as the others mentioned, it's one that would on occasion that would pop up every once in the while in the past for characters that struggling with not being able to have kids only to be hit with this trope for the sake of drama / sad feels.
But now, especially in LGBT+ media / characters (which I watch more often because, hell yeah representation), this particular plot/trope has been popping up more often, and it's the most frustrating and heartbreaking thing to constantly have to go through with so many LGBT+ characters.
I'm not sure what the name for it is but it's the very specific scenario of 'character can't have a baby of their own due to health, medical, relationship reasons and wants to adopt a baby. So they go through the steps to adopt and have been waiting and longing, finally they get a call, they're happy, their terrified, go through that conversation with loved ones and friends of 'what if I'm not a good parent' with their friends and loved ones being supportive and telling them 'don't think like that you'll be a great parent' then when they finally calm down and are ready to see the baby get the phone call that tells them "SORRY THE MOM CHANGED HER MIND AND IS KEEPING THE BABY"
Every. fucking. time.
It's a very very very specific scenario that for some reason just keeps happening in stories, and I can tell it's starting as soon as the character gets that damn phone call. The target for this trope is a very SPECIFIC, the sick/disabled that can't have their own kids and LGBT+ couples that want to have kids. It's punching down on characters who are already suffering for 'sad plot' and it just bugs me so much.