Thousands of Long Island homes damaged by superstorm Sandy are still not covered by flood insurance, leaving much of the region dependent on government aid if another catastrophe hits, a Newsday analysis of federal data has found.

Since the 2012 storm, the number of properties in Nassau and Suffolk counties covered by flood insurance has increased 9 percent, or by roughly 7,600 policies, according to the Federal Emergency Management Agency. That rise, however, falls well short of covering all 26,500 Long Island households that were uninsured when Sandy hit and received FEMA disaster assistance.

“There are people on Long Island who should be buying flood insurance and aren’t,” said Amy Bach, who runs United Policyholders, a San Francisco nonprofit that helps homeowners file insurance claims after disasters. “They are still depending on the government to bail them out.”

FEMA, which runs the National Flood Insurance Program, does not track whether every flooded homeowner later buys coverage. Nor does the agency have a town-by-town accounting of where uninsured storm victims resided.

So while it’s clear Long Islanders have not bought enough policies to cover every home damaged by Sandy, it’s difficult to determine exactly how many storm victims remain uninsured.

That’s in part because the number of those still unprotected by flood insurance was likely offset by factors that are challenging to track. In some instances, uninsured storm victims may have opted not to rebuild. And in other cases, homeowners who didn’t flood may have canceled policies.

Nonetheless, advocates for storm victim and insurance professionals said the discrepancy between the 26,500 uninsured homes flooded by Sandy and the 7,600 policies purchased since is cause for concern.

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“It potentially puts us right back in almost the same catastrophic category as we were in before the storm,” said Scott Primiano, an Amityville-based insurance agent.

Nationally, the picture is even bleaker.

Since Sandy hit, the number of properties covered by flood insurance has dropped 7 percent, as roughly 411,500 homeowners across the United States have let policies lapse. More than half were in Texas and Florida.

Officials attributed that drop to two primary factors.

For one, the National Flood Insurance Program has sharply increased premiums over the last year to comply with a 2014 federal law designed to help ease the government-run insurer’s $23 billion debt.

The other key factor, officials said, is that nearly a decade has passed since a major hurricane has hit Florida or the Gulf Coast, leaving many to underestimate their risk of flooding.

The result, industry experts said, is that the federal government and, ultimately, U.S. taxpayers may wind up absorbing the cost of rebuilding for thousands of homeowners the next time a major storm hits.

“This is a canary in the coal mine for the American taxpayer,” said Robert Hartwig, president of the Insurance Information Institute, a Manhattan-based trade group.

Most homeowners’ insurance policies do not cover flooding. In fact, the majority of private insurance companies do not sell the coverage at all, saying it is too risky.

So since 1968, the federal government has offered policies through the National Flood Insurance Program, now run by FEMA.

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The coverage is mandatory for anyone with a federally backed mortgage whose home is in a 100-year flood plain, which has a 1 percent chance of flooding in any given year based on its elevation and proximity to water. Yet that rule, which is supposed to be enforced by mortgage lenders, has long been widely ignored.

When Sandy hit, fewer than half of the homes damaged on Long Island had flood insurance policies. Consequently, more than 26,000 families were left largely reliant on FEMA aid and grants from the federally funded New York Rising program to rebuild their homes.

Three years later, Long Island is better prepared as thousands more homeowners have bought policies.

In some cases, the government has forced them to purchase coverage. For example, those in the 100-year flood plain were required to buy policies in exchange for receiving aid from FEMA. The same is true for anyone who took money from New York Rising.

In other instances, banks have forced homeowners to get flood insurance. After years of lax enforcement, the lenders are being adamant about requiring borrowers in the 100-year flood plain to buy coverage when they take out mortgages or refinance existing loans, according to insurance brokers.

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“It has become non-optional,” said Primiano, the Amityville insurance agent.

Yet the rules and the increased enforcement have not been enough to ensure every Sandy victim buys a flood insurance policy.

Flood insurance coverage remains optional for homeowners across Long Island. Sandy flooded thousands of properties outside the 100-year flood plain. And because they lived on higher ground, those homeowners were not required to buy policies — even if they received aid from FEMA. (They did, however, need to buy a policy if they took money from New York Rising.)

As a result, up to one-third of the 26,500 storm victims who were uninsured when Sandy hit still don’t have coverage.

Amy Bach, of United Policyholders, said part of the problem is homeowners have lost confidence in the National Flood Insurance Program.

In the year following Sandy, more than 2,000 storm victims sued the program in federal court, claiming they were underpaid. Those lawsuits led to allegations that private companies hired by the government forged documents to improperly deny settlements, prompting a state criminal probe.

FEMA has acknowledged that the program has a problem. In response, the agency launched a sweeping process in May to review up to 142,000 claims filed after Sandy. It found that roughly 60 percent of storm victims had been underpaid by an average $15,000.

“A lot of consumers have this general notion that the program is a rip-off,” Bach said. “It’s not true. But that’s a definitely perception.”