NEW YORK, JAN. 9 -- Grace Cheng, a waitress on her way to work, lost her life for $1 after a mugger grabbed her purse in a subway car and she leaped from the train after him, falling under the moving wheels, police said today.

Cheng, 31, who died Tuesday night after surgery on her partially severed leg, was carrying a dollar bill and seven credit cards in her wallet, said Sgt. Robert Valentino, a transit police spokesman.

Minutes after the mugging in the 96th Street station across from Central Park on Manhattan's Upper West Side, police arrested a man whom they saw run from the station and, after looking behind him suspiciously, rifle a wallet.

The suspect was identified as Brian Lawrence, 30, a New Jersey resident with a lengthy record of arrests over the last 12 years for robbery, bag snatching and failure to pay the subway fare. Many of his previous crimes also took place in the subway system, police said.

Police said Lawrence told the arresting officers, "I can't believe it. I'm in all this trouble for a $1 bill." Lawrence has been charged with robbery, assault and felony murder in the incident.

Citizen groups who keep an eye on the city's crime-plagued subway system, calling the events a tragedy, said they highlighted the failure of the criminal-justice system to keep repeat offenders off the streets.

"If you can't go to work feeling safe on the subway or walking through your neighborhood, why stay at your job or in the city?" said Joseph Rappaport, coordinator of the Straphangers Campaign, a subway riders' advocacy group. "This is as serious as it gets for a city fighting to stay a liveable place."

Cheng, who came to the United States about 10 years ago from Hong Kong, was riding the subway Tuesday morning from the Upper West Side apartment she shares with her mother to her job at a Japanese restaurant, relatives told reporters.

As the southbound C train left the station, a man entered the car where Cheng was sitting and, within seconds, snatched her purse from her lap, according to sources close to the investigation. As the train picked up speed, he fled through the door between cars and Cheng chased him, trying to leap onto the platform after him.

Cheng fell between the platform and the moving cars, suffering a broken pelvis, left thigh and arm and a partially severed leg, the sources said.

Edwin Pacheco, 42, and Felix Burgois, 35, unemployed security guards on their way to a job interview, witnessed the incident from the platform and tried to alert a conductor to stop the train, police said. The men jumped down to the track after the train had passed and lifted Cheng onto the platform. She was taken to nearby St. Luke's Hospital, where she died almost 12 hours later.

Police said Lawrence had a history of entering the subways without paying and of preying on subway riders in lightning-quick robberies. They said he was released from a state prison last July after serving a 4 1/2-year term for robbery in the subway.

The incident lent support to a current transit authority advertising campaign that encourages riders to help apprehend "fare beaters" because they might be guilty of more serious crimes.

"The people who are not paying their fare oftentimes are there in the subway not for transportation purposes but are involved in some kind of criminal activity," Valentino said.

"We have historically stopped fare beaters who have Uzi machine guns and other weapons. . . . Years ago, there was someone who was on the most wanted list who was picked up for fare-beating."