If someone lives in an apartment building with other Jews, do they need to make an eruv chatzeiros (in short: have shared food stored somewhere to make it considered as though they all live there together) to be allowed to carry from their apartment to the hallway or to neighboring apartments when the city's eruv goes down (after a storm or the like)?
The short answer is "Yes".
However, a premise in the question is erroneous. An ערוב חצרות is only necessary to carry from the common area into the private area. Therefore, without an ערוב חצרות, it is still permissible to carry within the hallway itself, and one could carry objects that remained in the common from the start of שבת within the common area such as playground toys. See O"C 366:1 & 372:1 and the משנה ברורה who explicitly permits this. See also באור הלכה on 372:1 about a מחלוקת with regard to items such as a scarf, coat or hat that were worn into the common area, and removed therein. However, one must be careful to then put them back on before entering the apartment.
NOTE: This is different than the strings and poles commonly used for encircling neighborhoods, colloquially called "eruvin". If the strings went down, then all carrying is prohibited even entirely within the public area, since there are no halachic walls. It is theoretically possible to have poles and strings without the ערוב חצרות, but that would probably be unlikely.
My grandparents used to live in such a building, where there was one other non-religious family in the entire building, so they never bothered trying to make an ערוב. It was our practice to follow the lenient opinion with regard to clothing worn into the hallway.