The crash happened just after 3 p.m. on Monday in the 13000 block of Whittier Boulevard, between Washington and Madison avenues, according to Whittier police.
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Video of the crash shows the woman get out of her parked car and then get hit by a dark-colored SUV that passed by. The victim immediately falls to the ground.
The suspect remains outstanding.
The victim, Lisa Park-Ortiz, was just about to start a new job next week, her aunt told Eyewitness News.
Park-Ortiz was taking her 8-year-old son to get a haircut when the crash happened.
"They didn't even hit the brakes. Her son, who witnessed her get hit, ran into the barbershop and asked them to call 911," said Mary Ann Grant, the victim's aunt.
Grant is asking anyone with information to come forward and call police.
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"I understand being scared, but you've had several days of carrying this on your conscious, and the weight has got to be very heavy," Grant said.
Park-Ortiz, a two-time cancer survivor, remains in the hospital with several broken bones.
"It's going to be a long recovery," Grant said. "She has a lot of breaks in the pelvis, vertebrae, a gash on her head that required five staples."
The family is taking donations for bills and rent via fundrazr.com.