This is the reversed Stockholm Syndrome. It was named after an incident in Lima, Peru where a terrorist cell held a few people hostage only to let them go after developing some sympathy and/or empathy to the captives. Which is weird considering you kidnapped them and held them for ransom or political gain or whatever.
There are a number of reasons why this would happen. Maybe one or more of the kidnappers don't agree with the plan, or they just don't feel up to hurting innocents. Maybe they just had a change of heart. It's normally the person in charge that would develop this, but it doesn't exclude henchmen.
In Disney's Beauty and the Beast, (yes this again)Belle agrees to be the Beast's prisoner in exchange for letting her father go. When he puts her happiness ahead of his own, he eventually lets her go too. She returns to him later to help him, but this is because HE has made the greater improvement in his attitude towards her. By the film's own admission it was he who first fell in love with her, and Lima Syndrome is more prevalent than the Stockholm Syndrome some believe is at work. It is worth noting that the movie takes place over several months, so who the hell knows.
In The Legend of Korra, Ikki is captured by two Earth Empire soldiers, who originally plan to find her siblings and deliver all three to Kuvira. However, Ikki is both sneaky and legitimately friendly enough that, as she talks to them more, they seem to forget their previous idea and actually give her information that helps her on her mission to find Korra. When her siblings bust her out, she feels so bad about them getting knocked around that she leaves them a couple of buns in thanks.
Now writing this is a bit tricky, for many reasons. One being it sometimes pop up in situations of the adult variety that involves abuse. Now I'm not saying its a problem, but if it looks like a duck...Writing situations involving this doesn't have to have a romantic element, it's a cliche. It can be a sympathetic lean towards a hostage who just so happen to be pregnant and suffered many miscarriages, a child, or even a person that reminds you of someone you know and somewhat care about.
I'm just saying....if you can write a story where the baddie changes their mind because a child convinced them somehow, you are a treat.