About 1,700 people rejected for the Reconstruction, Rehabilitation, Elevation and Mitigation (RREM) program and 2,000 rejected for $10,000 resettlement grants did not appeal their denials.
About 7,000 people remain on the RREM waiting list.
"We're glad the administration has just changed its position," said Kevin Walsh of the Fair Share Housing Center in Cherry Hill, which uncovered the error rate. "It's better late than never. The big issue now is to make sure that people who were unfairly denied don't get put in the back in the line."
Legislators scheduled a committee meeting for Tuesday to hear testimony regarding problems with Sandy homeowner relief programs.
Gov. Christie, who encountered a frosty reception from frustrated Sandy victims at a stop this week in Keansburg, scheduled a Sandy town hall meeting in Port Monmouth for Thursday.
The Sandy aid programs - criticized from the start by victims as inefficient, slow to deliver meaningful help, and confusing - have been the target of criticism on a variety of new fronts.
Those include the state's quiet firing of its largest contractor overseeing aid programs, allegations that Christie officials had tried to leverage unrelated deals with Sandy aid, and use of federal money in places where little, if any, damage occurred.
In the latest issue, cited Wednesday by the Fair Share Housing Center of Cherry Hill, the state Department of Community Affairs had acknowledged the error rate, but blamed data from FEMA.
FEMA, in turn, said the state misused its data, which it said was meant only for emergency assessments for long-term rebuilding criteria.
Housing advocates cited New York's plan for Sandy recovery, which takes the limits of the initial FEMA data into account. New Jersey's did not.
The Fair Share Housing Center, along with Sen. Jim Whelan (D., Atlantic) and other legislators, had called for the appeals process to be reopened.
But on Thursday, state officials said they would not reopen the appeals, saying all those denied had received letters explicitly citing the FEMA data as the reason and inviting them to appeal. They cited the need to curtail waste, fraud, and abuse and expressed confidence that those wrongly ruled ineligible had been given ample opportunity to appeal. The FEMA data were used to establish an $8,000 threshold of damage for eligibility for the program.
But late Friday, Constable reversed course, issuing a statement that said: "We want anyone who is eligible under the guidelines to have a full and fair opportunity to receive assistance. Therefore, applicants who were deemed ineligible and did not appeal that determination will shortly receive a letter that outlines the steps they can now take to file an appeal."
Applicants can find the appeals work sheet on the www.renewjerseystronger.org website.
The DCA says about 5,100 Sandy-impacted homeowners have so far been approved for a RREM award. Grant award signings have been completed with about 1,200 homeowners, obligating more than $137 million in aid.