State and local governments are cracking down on people for improperly claiming something called the homestead exemption. Take Representative Charles B. Rangel of New York, who was accused of doing just that on a home he owns in Washington, D.C.

But as the tax authorities look for cheats, they are finding that many people who are eligible for homestead exemptions fail to apply, even though the exemptions can provide valuable breaks on property taxes — the issue in Mr. Rangel’s case — as well as protection from creditors.

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