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The $10,000 home — rare? Not in Detroit, the largest American city to enter bankruptcy — in its case Chapter 9. Realtor.com lists 515 homes for sale at between $5,000 and $10,000.

Most of these low-priced homes are small, as measured in square footage. Many are fewer than 2,000 square feet in size and have two bedrooms or less. Many also sit on lots that are less than 4,000 square feet — barely large enough for a real yard.

A great many of the cheap homes are clustered well outside the center of downtown, which sits on the Detroit River. There have been some partially successful efforts to rebuild this city center. And the sections of the city between General Motors Co.’s (NYSE: GM) headquarters in the 73 story Renaissance Center and Comerica Park where the Detroit Tigers play, and Ford Field, which is the home of the Detroit Lions, have been improved — or at least have not fallen apart further in the past 10 years.

The Detroit neighborhoods with cheap home prices are mostly northwest of downtown toward Eight Mile Road, which is the northern edge of the city. A great many of these homes were built before World War II, probably for people streaming into the city to get automotive assembly plant jobs. Many of the neighborhoods where these houses are located have been almost entirely deserted.

Detroit is a huge city geographically. It covers 139 square miles. The population in the city has dropped from 1.5 million in 1950, to less than 750,000 today. The decline in the number of residents accounts for most of the vacancies.

One theory about how Detroit’s vacant sections can be “rehabilitated” is through programs that would bulldoze most of these neighborhoods into the ground — flat tracks of nothing other than dirt or fields. The problem with the idea is that some of the sub-$10,000 homes are near enough to these areas (or located in them), that these few remaining residents would lose city services. In essence, Detroit would entirely abandon some of its population.

The greatest problem for Detroit’s low-end real estate market is that no one wants to move into the neighborhoods with sub-$10,000 homes. A bargain is only a bargain if someone takes it.