Slums, decaying low-income urban zones, are one of the worst possible locations to find yourself in during a zombie outbreak, second only to Hospitals.
As explained in World War Z, outbreaks usually start around hospitals, because that it where sick people bitten and infected by zombies will be taken, and then reanimate as zombies themselves. But slum districts of major cities are the next major location that early infections usually radiate out from.
The reason behind this is simple: slum districts are where people normally go when they want to hide, i.e. illegal immigrants. In World War Z, when infected people from China flee to other countries to seek treatment (in vain), they don't want to be caught by authorities screening for infected people but still desperately hope for a cure. So they go to the places that illegal immigrants normally go to hide: Chinatowns and other slum districts in major cities. Such areas also have relatively low police response or resources. The infectees are actively trying to avoid being caught, which specifically makes them less hard to notice when they turn. In World War Z, the first publicly known large-scale outbreak occurred in the slums of Cape Town, South Africa, even though the epidemic began in China - spread there by Chinese refugees.
As seen in Fear the Walking Dead, people living in slum districts (particularly immigrant populations) are more used to being harassed by the police, so rather than inherently trust a sudden declaration of martial law and mobilization of the national guard, they will distrust that things so far-fetched as "zombies" even exist, or even riot to oppose what they perceive as an unprovoked police crackdown. This hinders even further what little police/military response can be mustered towards slum districts.
- Slum districts are one of the first places that zombie infectees will try to hide after hospitals: particularly if they entered the country as refugees looking for a cure. If hospitals realize in time what is happening (before they are overwhelmed) and start screening for and terminating new infectees who arrive, local infectees will start hiding out in slum districts as well. It's where people go to get "off the grid" when they don't want to be found.
- Low building code standards means that many buildings are dilapidated and in a poor state of repair, such as with broken locks and doors. As a result buildings are difficult to secure.
- Low coverage by civilian police and emergency response resources, meaning these will be among the first places overwhelmed. For that matter given that they contain little vital infrastructure such as power plants, etc. police/military response will probably be prioritized elsewhere.
- Widespread distrust of civilian authorities by local population will only hinder police/military response to zombie outbreak, possibly with outright riots (not realizing what is really happening).
- Particularly slum districts that harbor illegal aliens will be active in various illegal activities, i.e. they're more likely to have hidden caches of illegal military-grade firearms than a suburban area or business district. But it really isn't worth trying to find them in the early days of an outbreak when slums and hospitals are ground zero for the epidemic.