Mother:

Sadako Aokigahara

Quirk: Chemistry Solidification

User can solidify or give solid-like properties to chemicals and chemical substances with the level of solidity going from loose jelly to metal-like hardness or beyond.

What Happened:

Before Sadako met Natsumi's father, she was a chemist and was a fairly well off woman for it. However when she got married and had a baby, she quit her job to stay at home with her daughter since her husband was in the army and someone needed to watch the baby. 

She had given Natsumi to a group home when she was two years old, and she had every intention to come back for her. The plan was to put her in a place where she had a roof over her head as she got on her feet, since she didn't have any money to take care of herself let alone her baby. 

It started out as a selfless woman sacrificing what she wanted for what was best for her very young daughter. 

She was homeless for two more years before she found a job and she found an apartment to live in before she found a man that she had fell for, and we was a wealthy business man. She hadn't told him about her daughter until she got married to this man she fell in love with. 

When she told him about Natsumi, she was already married to him and he was furious to know that she had been married and had a child with another guy. So, he gave her an ultimatum. Stay married to him in comfort of her new life where she can have whatever she wants, or get Natsumi back and be left on the streets again leaving her at square one. 

She chose staying with him instead of going back for her daughter like she planned. She convinced herself that she did it for her daughter's sake, instead of admitting that she was loving her luxurious new life and didn't want to give it up. 

She never had any other children either because while she was married to her new husband, she had developed cancer in her reproductive organs so they had to take them out so she wouldn't die from it. 

Father:

Hitori Aokigahara

Quirk: Slime Manipulation

User can create, shape and manipulate slime, ooze, and goo of every consistency or viscosity, whether sticky, slippery, etc.

What Happened

Hitori was part of the Japanese Army while he was married to Sadako as a soldier, often seeing horrific things regarding the battlefield including people that he got very close to die at the hands of the enemy. It was very traumatic for him, and when he left the army he developed PTSD, making the family dynamic go a little wild.

He was forced to leave the army, because while he was on the field he got shot in his right hip, and he got a limp making him unable to continue being in the army from this disability. He was devastated about this, and Sadako his wife tried to cheer him up, but he would only blow up at her in front of Natsumi sometimes. 

After the army, he was hardly ever home because he didn't want to blow up at his wife. He was often at bars, and had a gambling problem where he blew the money they needed for basic necessities on bets. He was a terrible gambler, but he was more worried about numbing the pain of what he went through, and feeling like a failure because he "let himself" get disabled. 

One day, he had gotten into an altercation with the police -again- and this time he fought back the officer from being heavily drunk and wasn't thinking right, landing him in an overnight jail waiting for someone to bail him out. This gave him time to think, too. 

He looked at what he was doing to Sadako and their one year old Natsumi. He was always going out, blowing all of their funds and being an overall horrible husband and father. So, after Sadako bailed him out of jail two days after, with his Mom looking after Natsumi, he tells her that he wants a divorce. 

He doesn't explain anything other than he's going to stay with his Mom and that she gets to keep everything, including Natsumi -even going as far as to forfeit his right as her father- not speaking to her unless through their lawyers. He left her with the house and everything, just to get the whole thing over with. 

However, his Mother had other plans and harassed Sadako blaming her for abandoning him while he needs her the most, even though he's the one that filed for the divorce. His Mom had framed Sadako for coming in and robbing her house and sued her and won, stripping Sadako for every penny she had leaving her and Natsumi homeless. 

While that was going on, Hitori had no idea what his Mom was doing and thought that his ex really had robbed his Mother and he actually called her to yell at her. Again, being highly drunk and still drinking. 

A year after he had divorced his ex wife and forfeited his rights as a father to his daughter, he had come across someone who he owed money to from losing a bet a week before. He didn't have the money, and no one that he knew would loan him anymore money since he blew it all on these bets to begin with. 

The thugs, decided to take his life as payment for the bet. They shot him in the head and left him in a dumpster near the casino. They thugs were caught, and Hitori was cremated and his ashes are at his mom's house to this day. Who blames Sadako for him being murdered and claimed that she had sent the people to kill him. But, she couldn't prove it to the police so she now wallows in bitterness for her son's ex-wife.