Her mother was in a car accident and suffered brain damage after her head went through the windshield of her car.
"She was never the same after that," Haddish tells PEOPLE. "She wasn't normal anymore."
As the oldest sibling, Haddish became the caretaker for her two sisters and two brothers.
"I was basically a 10-year-old mom," she says. "I was feeding them and dressing them. I was taking care of everybody."
That included her mother.
"I was suddenly having to teach her how to tie her shoes," says the actress. "Everything my mom had taught me for the first nine years of my life, now I was teaching her."
Haddish's new normal left her feeling overwhelmed at home and struggling to fit in at school.
Things got worse for Haddish when, at 12 years old, she was separated from her siblings after they were put in foster care.
"My sisters were placed together and my brothers were placed together but I was on my own," she explains. "The social workers had to stop telling me where they were because I would just get on a bus and go to them. I felt responsible for them."
Forced to attend a new middle school, Haddish would also leave her foster home at 5 a.m. and take a bus to her old school, where she felt more at home.
"My foster parents would report me missing when they got up and the police and my social worker would come get me at the school," she says.
In an attempt to make friends at her new school, Haddish decided to follow the advice of her favorite character from her favorite movie: Rodger Rabbit.
In Who Framed Roger Rabbit, the detective asks Roger, 'Why are people doing all this nice stuff for you?' And he says, 'Because I make them laugh. If you make them laugh, they'll do anything for you.' That stuck with me."
But cutting up in class got her sent to the counselor's office more than once.
"I was a weird kid. I'd make up imaginary friends and talk to them to make the other kids laugh," she says. "I just thought it was funny, but the teachers thought something was wrong with me."
By the time she was 15, she was reunited with her siblings and was being cared for by her grandmother. But her social worker was still concerned about her behavior.
"My social worker gave me two options: Laugh Factory camp or psychiatric therapy," says Haddish. "I said, 'I don't want to be put on drugs so I'll take the Laugh Factory.' "
At the Laugh Factory – a famous Los Angeles comedy club – Haddish says she learned "when and how to be funny" and was mentored by a revolving door of celebrity guests including the Wayans brothers, Dane Cook and Richard Pryor.
"Dane Cook said I had something special. Someone like that had never said anything like that to me before and I couldn't believe it," says Haddish. "Richard Pryor came in in his wheelchair. I thought all rich people must have wheelchairs and I wanted one. He told me, 'If you're not having fun, the audience is not having fun.' That is something I keep in mind both on stage and off now."
Participating in the weekly camp also provided Haddish with a celebrity encounter that she'll never forget.
"Charles Fleischer [who voiced Roger Rabbit] came in one day and when he did the voice I just started crying," she says. "I ran up to him and hugged him and thanked him for all he had done for me."
Haddish developed an ongoing friendship with Fleischer and she still considers him a mentor to this day.
"That summer changed my life," Haddish says of her time spent at the Laugh Factory. "It set me on the path to get where I am today."
Chris Haston / NBC
"It's so nice. The things people tell me about the show – how they identify with it and are connecting with it – mean so much to me. I couldn't ask for a better opportunity to be a part of."
But even as she experiences the biggest success of her professional career, Haddish does not forget the painful and humble beginnings of her journey.
"I know not everyone's story ends up like mine has – that is not lost on me," she says. "I was just a weirdo trying to find my way and I was given help exactly when I needed it. I was lucky."