WASHINGTON — The Supreme Court on Tuesday rejected an effort to change tax foreclosure sales to let homeowners to keep more money when their property is sold to recoup unpaid taxes.

The high court ruled against a Michigan family whose house was sold for less than half its open-market value to cover an unpaid tax bill of just over $2,000. They argued the foreclosure violated their rights because the house would have fetched a higher price of nearly $200,000 if sold through typical real-estate channels.

But the county maintained that auction sale prices are always lower than open real estate transactions, in part because they typically require full cash payment rather than a mortgage.

Requiring foreclosure sales to match open-market prices would essentially end them, making it harder to collect unpaid taxes, Isabella County argued.

The case comes about three years after another major foreclosure case where the justices ruled against local governments. The court found counties can’t keep tax sale proceeds beyond what the owner owes in unpaid taxes.

That case centered on a 94-year-old Minnesota woman whose county government kept about $40,000 in proceeds from the sale of her condominium after she failed to pay about $2,300 in taxes.