ATLANTIC CITY — It started slowly, with only 300 to 500 people a day coming in to take advantage of a program that could help wipe the slate clean for individuals dodging warrants for nonviolent offenses.

But on Wednesday, with the close of New Jersey's fourth — and probably its final — Fugitive Safe Surrender event drawing near, more than 1,000 people came "out of the woodwork" to have their paperwork processed by the 4 p.m. deadline, according to law enforcement officials.

Program administrators estimated that the final tally for the event that began Saturday — Sunday was a non-service day because the intake area was at an Atlantic City church — would exceed 2,700. The official total will be announced Thursday.

"Everyone always seems to wait until the last minute," said Martin Houston, a spokesman for the New Jersey State Parole Board. "We think they want to check it out and make sure it's not a sting operation. Word gets out that people aren't being incarcerated, and they are leaving with good deals."

Those eligible for "good deals" included people charged with motor vehicle violations, failure to pay child support, and disorderly persons charges who have remained fugitives because they feared going to jail or did not have enough money to pay fines.

Though Safe Surrender is not an amnesty program, authorities said that those who come forward voluntarily are given favorable consideration by the court system with reduced fines, payment schedules, and, usually, no jail time. About 10,000 people have stepped up since the program was introduced in New Jersey in 2008, and only about 1 percent have ended up in the slammer, officials said.

Worry that he could end up in that unlucky group led Mafousa Betts, 29, of Atlantic City, to delay until late Wednesday to show up. He had checked with friends and a lawyer, he said, about whether he might be hauled to jail on three warrants for traffic violations that had been "floating around the court system" for five years.

After making a small payment toward the $500 in fines he was told to pay — about a third of what he would have owed otherwise — Betts walked out a free man.

"I feel so much better ... so much better than when I came in here," said Betts, who had a wide smile despite the tears in his eyes.

Participants registered at the Grace Assembly of God Church on Atlantic Avenue before being transported by jitney to one of a dozen makeshift courtrooms at the Atlantic City Convention Center. On Wednesday, some waited as long as three hours to have their case heard before a judge.

Officials said most of the Safe Surrender participants came from Atlantic County, where there are about 117,000 active traffic and criminal warrants. Some arrived from as far away as California and Florida. Only one person — who faced a sexual assault charge — was taken into custody, officials said.

"Usually when individuals with charges like that turn themselves in, they know ahead of time it's going to happen ... but they find themselves tired of running or hiding," Houston said.

Started in Cleveland seven years ago to reduce the risk of violent confrontations when a police officer serves a warrant or encounters a fugitive in a routine traffic stop, the program has netted approximately 40,000 people wanted for nonviolent offenses. In New Jersey, the program has saved the state an estimated $1.5 million in court costs. Safe Surrender events in New Jersey also have been held in Camden, Newark, and New Brunswick.

Funding for the program, which had been provided by the U.S. Marshals Service, has dried up, making the event in Atlantic City the final one for the foreseeable future, Houston said.

Contact Jacqueline L. Urgo at 609-652-8382 or jurgo@phillynews.com. Follow her on the Jersey Shore blog "Downashore" at www.philly.com/downashore.