In the ensuing years, the city’s real estate was transformed into an Alice-in-Wonderland-like landscape. Local officials began keeping track of foreclosed homes by placing red dots on large wall maps. Some corners of the map, like Slavic Village, are now so packed with red dots they look like puddles of blood. The first question outsiders now ask is, Where has everyone gone? The homeless numbers have not increased much over the past couple of years, and it appears that most of the people who lost their homes have moved in with relatives, found a rental or moved out of the city altogether. The county has lost nearly 100,000 people over the past seven years, the largest exodus in recent memory outside of New Orleans.

Banks are now selling properties at such low prices — many below what they sold for in the 1920s — you have to wonder why they bother to foreclose at all. (The F.D.I.C. estimates that each foreclosure costs a bank on average $50,000, more than if they were to do a loan modification.) All of this leaves Brancatelli in a constant state of exasperation. When asked how he’s doing, he often takes a breath and replies, “Another day in paradise.”

O.V.V. IS A TERM OF ART that stands for Open, Vacant and Vandalized. Houses fitting this description have popped up like prairie dogs. They are boarded, unboarded, then boarded again, and the city can’t keep up with the savvy squatters. They will prop the plywood over the front entrance to make it look as if it’s nailed shut. One woman told me that she called the police last summer when she saw smoke coming out of a vacant home across the street; it turned out that some young men were cooking on a grill inside.

On a dreary wintry day, Brancatelli took me to Hosmer Street, on which a fourth of the homes were foreclosed. As we strolled down the block, Brancatelli noticed something odd. Through a side window of one slender house, we could make out a waist-high pile of tree limbs and branches. The front door was off the hinges and propped against the entrance. We entered through the rear, where the door was gone altogether. “Hello,” Brancatelli hollered, “City!” — an effort to both warn squatters and frighten animals. Earlier that day we entered another O.V.V. and heard footsteps upstairs. “They don’t have a gun,” he had assured me. He explained that scavengers know enough not to carry weapons because it would mean more prison time should they be caught. Even in O.V.V.’s, there are rules.

Inside, we found firewood and brush piled in the kitchen and front room. “The crap we deal with,” Brancatelli muttered to himself. He snapped a photo with his cellphone and sent an e-mail message to the city’s Building and Housing Department, urging the department to send someone to secure the house. He often does this two or three times a day. But finding a collection of timber like this is of particular concern; over the past year there have been more than 60 fires in his ward, all in vacant houses. The fire department tried stakeouts but has not caught anyone. The general belief is that the fires are set either by squatters trying to stay warm or by mischievous kids. Brancatelli, though, wonders aloud if it might be vigilantes who don’t like the blight on their block. “Maybe I’m overthinking it,” he says. More likely, he’s projecting. He would like to see many of these houses just disappear.

This is Brancatelli’s conundrum: many of the abandoned homes should be razed. They’re either so old or so impractically tiny that they have little resale value, or they have been stripped of their innards and are in utter disrepair. There are an estimated one million lender-owned properties nationwide, and on average each house sits empty for eight months, a length of time that is only growing. Demolition, though, is costly: roughly $8,000 a house. Two years ago, Litton Loan Servicing, a mortgage servicer, discussed giving the city a number of foreclosed homes. Free. The city told them that would be fine, but only if the company came up with money to pay for the necessary demolitions. The transaction never occurred.

Image City Councilman Tony Brancatelli and other officials in Cleveland are grappling with at least 10,000 abandoned homes, many owned by lenders or speculators who trade them like baseball cards. Credit... Reuben Cox for The New York Times

Last summer, Congress appropriated $3.9 billion in emergency funds for cities to acquire and rehab foreclosed properties. (An additional $2 billion will be available under the recently enacted economic-stimulus package.) The legislation was labeled the Neighborhood Stabilization Program, but Cleveland and a handful of other cities had to lobby hard to convince Congress that “stabilization” in their cities meant tearing down houses — not renovating them. Last month, Cleveland said it planned to use more than half of its $25.5 million allotment to raze 1,700 houses. This presents an opportunity to reimagine the city, to erase the obsolete and provide a space for the new. (There’s little money now to build, so imagine is the operative word.) Cuyahoga County is also establishing a land bank, a public entity that can acquire distressed properties and hold on to the land until improved economic times allow for redevelopment. The county hopes to persuade banks to unload their distressed properties, which the land bank would then raze, as well as give up some foreclosed properties in the suburbs, which the county could eventually renovate and sell.