Officially the Men in Black agents do not exist. No paper trail or forensics of them can be found. So one has to ask how does J and likely every other agent have a home to live in when not on shift?
Although it's not confirmed in the films (or their accompanying novels), the reality seems to be that MIB probably own and operate the apartments that their Agents live in.
Z: You will conform to the identity we give you, eat where we tell you, live where we tell you
The most obvious evidence for this is the large armoury found in Agent K's old apartment. It seems very unlikely that K would have had the personal skills to install and equip such a large add-on without at least consulting with his superiors.
J's apartment (from MIB:3) seems spartan to the extreme. Basically just somewhere to sleep and chill before returning to work in 8 hours. Note that it's also in the standard MIB monochrome colour-scheme.