SOME 12 MILLION American households are poor enough to be eligible for federally subsidized housing. By one estimate, that figure will rise by 5 million in the next 20 years. But the same study says that the nation's low-income housing stock -- now about 12.9 million units -- will shrink to 9.4 million during the same period. For years the basic argument about federally subsidized housing was over the rate of increase in the number of new units. But the country now faces the problem of how to prevent a dramatic decrease.

Since 1976, thousands of low-income Americans have been housed through 15-year federal rent supplement contracts that will begin to expire in 1991. But another 700,000 low-income tenants have been living in housing that was subsidized by previous federal programs, and they could be displaced as early as 1989. Those 700,000 people were beneficiaries of federal programs that gave private owners an "up front" subsidy or monthly payments to reduce their mortgage interest rates. The owners then agreed to house lower-income families in their units. Although the mortgages were generally subsidized for 40 years, several owners -- with as many as 334,000 of the units -- will be able to prepay their mortgages after only 20 years. When that happens, the owners will no longer be obligated to rent to lower-income tenants.

Federal officials say that only 10 percent of the owners involved in the mortgage subsidy programs have sought higher-income families. Their recommendation has been to give the poor housing vouchers that are good for five years. But that will not be adequate with so many federal housing programs due to expire at the same time. Congress and the administration have been evading an important question -- what to do about people at the bottom end of the income range who will not be able to afford a rental of an apartment or a house of their own. Housing was one of the major federal programs for the poor that suffered deep budget cuts. The cuts went too far. It will be costly, but the next administration is going to have to answer the question currently being ignored: Where will the poor live?