One of the questions that surfaced following the death of Police Officer Kevin Lee on Friday is why two of the suspects not only have extensive criminal records but live in publicly subsidized housing in Brooklyn.

Lee, 31, died after collapsing during a pursuit of three male suspects who were allegedly shoplifting on the Upper East Side.

The three suspects, police said, in the past have been arrested for, among other things, grand larceny, robbery, forgery, burglary, resisting arrest, and narcotics charges.

Two of the suspects, Lorenzo Walters, 18, and Julio Marquez, 19, live in a Brooklyn public housing development, Gowanus Houses; the third suspect, Rico Banks, 19, lives in a private building in Queens.

“The city would have been able to take proceedings” to evict them if there were convictions on those prior charges, said Dennis Saffran, an attorney who represented public housing tenants who were pressing for the eviction of drug dealers about a decade ago.

But that’s if the city knew about the convictions. A spokesman for the New York City Housing Authority, Howard Marder, said that once people reside in a public housing development, management does not check their criminal records routinely. “With more than 420,000 residents we couldn’t physically do annual background checks,” Mr. Marder said via e-mail.

However, residents can be evicted under certain conditions: For example, if “the premises, or any part thereof, are used or occupied as a bawdy-house, or house or place of assignation for lewd persons, or for purposes of prostitution, or for any illegal trade or manufacture, or other illegal business,” according to The New York State Real Property Actions and Proceedings Law.

Carl Callender, executive director of Queens Legal Services, said the housing authority has “been pushing out a lot of people with criminal histories.” His organization represents between 10 and 20 tenants each year who face eviction for a number of reasons, including an alleged fight with another tenant, an alleged robbery near the premises, and a drug arrest in or around the housing development.

There has been much debate about whether a tenant should face eviction if a guest or relative commits a crime on the premises. “The person living in public housing would not be evicted,” assured Mr. Marder. But the guest or relative convicted of the crime could be excluded from a lease and banned from the premises as a condition of the tenant’s lease, he said.

A candidate may be ineligible to live in public housing because of a criminal background. Level 3 sexual offenders, designated “high risk” by New York State law, for example, are legally barred from living in public housing. Federal law says that owners can deny admission to a public housing program “on the basis of drug-related or violent criminal activity,” according to the 2001 Federal Register.

A civil rights activist, Norman Siegel, said any move to withhold housing from people with a criminal record or even to prevent them from visiting their families in a public housing development further penalizes a convict. “You have to give them a second chance,” he said.

In the case of Mr. Walters, Julio Marquez, and Rico Banks, a Manhattan grand larceny team saw them at about 6 p.m. Friday, entering and exiting five stores along Lexington Avenue, starting at 69th Street, police said. When the suspects left Snappy Auctions, at 1236 Lexington Avenue, Officer Lee, two other officers, and their sergeant found out one of the suspects had stolen a laptop from the store, police said. The team swooped in to arrest the suspects in front of 150 East 86th Street, when “a struggle ensued,” according to the police commissioner, Raymond Kelly. Officer Lee, a 10-year veteran, collapsed, and after an attempt to resuscitate him, police said, he was taken to Lenox Hill Hospital, where he was pronounced dead at 7:55 p.m.

Messrs. Walters and Marquez were charged with robbery, coercion, grand larceny, criminal possession of stolen property, and resisting arrest, police said. Mr. Banks was charged with robbery.

The cause of Officer Lee’s death was not yet determined yesterday, according to a spokeswoman for the medical examiner’s office, Ellen Borakove.

“While the cause of Officer Lee’s death is still uncertain, [last night’s] events remind us once more how death can strike at any time,” Mr. Kelly said at the hospital on Friday. “And in this instance, taking the young life of a police officer doing his job.”