The obvious answer is "Because without maintenance and occasional renovation everything old gets rundown." Of course that avoids the issue of why old neighbourhoods tend to enter a phase where everyone stops doing that maintenance and renovation. To a large extent, that's because of real estate depreciation. Even with maintenance, property values tend to steadily go down over time. As the price to live there gets cheaper, more and more people living marginal existences move in and with them come the people who prey upon those people. Those people tend to be less likely to maintain their property so they neglect it and of course that drives real estate values down even further and the more entropy they see around them the more people are inclined to just give up and let it go. This trend tends to continue until something happens like artists making an area hip, or a real estate guy taking advantage of the low property values to do some king of major development that will level most of the neighbourhood and push the marginalised inhabitants into some other neighbourhood on the downward slide, continuing the cycle.
Public squalor, rundown section of a city
old rickety wobbly rundown
Neighborhoods away from the city centers
Slum
slum
The FHA program for financing home improvement is actually a group of programs that are offered by the U.S government to refresh the rundown of neighborhoods in cities across the United States.
Neighborhoods away from the city centers -Apex
A rundown neighborhood is known as a slum or a "ghetto" (ghetto does have racial overetones). In the 1900's when the huge wave of immigration started to the US, the term used was "tenement housing" especially in New York City. There was poor light, sanitation and incredible overcrowding. One of these buildings in NYC is now The Tenement Museum, which is a fascinating thing to visit.
Montevideo is a city itself so it has neighborhoods inside.
A suburb is an area on the outskirts of a cityAn area or community located outside of, but near a larger city or town.outside a city or town
rundown means a building
She did her inventions in her "laboratory" which was an old rundown garden shed.