FOR YEARS, flooding along Four Mile Run kept rents so low in the Arlandria section of Alexandria that it became a tenant's haven for some of the area's poorest immigrants. Those times have changed.

A $59 million federally financed project has eliminated the possibility of more flooding, and city officials have taken another look at this long- neglected community and want to rejuvenate it. Assessments on houses have quadrupled. Property values along one Arlandria thoroughfare have jumped from $3 per square foot to $20, and developers want to convert several apartment complexes into more luxurious residences while adding restaurants, office space and shops.

That will bring new life to a depressed area -- but it will also create problems. Plans to upgrade about 75 percent of the area's rental stock have raised concern that as many as 3,000 people may be displaced.

There is no place in Alexandria for a large number of displaced residents. The city's vacancy rate for apartments is only 1 percent. In that respect, Alexandria illustrates a squeeze on low-income families that has become common across the country. In the past, more federal funds were available for everything from low-income housing construction to Section 8 subsidies to landlords with low-income tenants. Those times have changed too.

City officials say the best hope is with investors who buy apartment complexes in Arlandria and apply for tax-exempt financing. That would require them to maintain 20 percent of the housing at lower rents, based on 80 percent of the Washington areas's median income. But that alone is no guarantee. That median income figure is about $29,000, far more than most Arlandria residents earn.

The investors who bought Arlandria's Presidential Gardens apartment complex want tax-exempt financing. Fortunately, Alexandria officials are taking an imaginative look at options and incentives that may prevent wholesale displacement. Income surveys are being done to determine what residents can afford. Rezoning may offer higher-density units in exchange for keeping low-and moderate-income units. A system of tiered rents is also being considered.

By one estimate, there was, nationwide, a net loss of 500,000 rental housing units per year in the 1970s, mostly in the lower-rent range, through displacement, condominium conversions and demolitions. Nationally, 55 percent of the 8.5 million low- income rental households that earn $7,000 a year or less are paying 60 percent or more of that income for housing. In the absence of further federal initiatives, the housing of low-income families will depend increasingly on the concern and imagination of local governments like Alexandria's.