Police in California said they are searching for a motive after arresting a 24-year-old man for allegedly setting a homeless woman on fire as she slept on a bench in San Fernando early Thursday morning.

The 67-year-old victim remained hospitalized and was listed in critical condition.

Authorities said a man, identitied as Dennis Petillo, dumped flammable liquid on the woman and lit a match around 1 a.m. outside a Walgreens pharmacy.

Officials did not release the homeless woman’s name; however, the Los Angeles Times reported that she has been a staple of the neighborhood around Van Nuys Boulevard and Sherman Way, where she bought a pack of cigarettes every morning.

Community members said the woman's name was Flo Parker, but she went by Violet. Some noted her kindness as police continued to search for a motive behind the apparently random attack.

"There was no incident or dispute or clear motivation for this horrific attack. He did not know his victim. It defies explanation," LAPD Deputy Chief Kirk Albanese said, before elaborating on Petillo. "He is not of sound mind ... The motive is mental illness."

Erickson Ipina, a witness, the the newspaper that he watched as a man came out of the Walgreens, carrying what appeared to be a bottle of rubbing alcohol.

“He just poured it all over the old lady,” Ipina said. “Then he threw a match on her and started running …I  pulled out my cellphone and called 911, and then he just turned his back on me and pulled out a knife.”

Few details were available as to why "Violet" was living on the streets. She almost always spent Wednesday and Thursday afternoons eating a free lunch, provided by Central Lutheran Church.

Groundskeeper William Gonzalez, who said he knew "Violet," said she had previously worked as a nurse and was the mother of two children.

"She never had a bad word for anyone," he said. "She smiles and says, 'God bless you' to you. She never, ever asked for change."

In recent months, L.A.’s treatment of its homeless community has come more sharply into the spotlight. One man was set on fire while sleeping outside a donut shop last week, according to CBS.

Two months earlier, police arrested Jacob Timothy Lagarde, who they said threw a Molotov cocktail at a man.

The city of Los Angeles has long been known for its large homeless population. Hundreds of people struggle to survive in its Skid Row area. Conflicting census reports have estimated that the Skid Row homeless population alone is close to 5,000 people.