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There is either insufficient or no garbage collection services available - either the collectors are on strike or the city grew a lot faster than the local government can keep up with demand (i.e., rapidly urbanizing Third-World cities).
Subverted: The character opens the door, and we see what appears to be a scene of Trash of the Titans squalor, but it's revealed that this is actually the result of vandalism, or that it's not really his home, or any other situation where Trash of the Titans doesn't apply.
Double Subverted: Bob brings Alice back to his apartment, and her reaction to the trash is very negative. However, Bob acts shocked about the "vandals who destroyed his house," and Alice believes him, though it actually was just Bob having a really messy house. (This was, of course, the plot of a certain Snickers commercial.)
The character decides that if he's going to live like this, he might as well get paid for it, and rents his living space out for purposes of storing garbage.
Conversed: "I love it when these TV shows not only drop the shiny, artificial image of keeping everything clean, but go to the opposite end of the scale and have everything be over-the-top dirty. Kind of like you and me, come to think of it."
Deconstructed: The plot centers around the Health Department preventing the community from suffering the dangers of places like this. Perhaps even with the health inspectors as the main characters, rather than the messy residents or their acquaintances.
Reconstructed: The character in question turns to be diligent and extremely resourceful recycler/scavenger. The piles of "garbage" he has gathered are in fact usable/useful stuff that careless/wasteful people has thrown away, and which the character cleans, repairs and repurposes so that they might be used once again by him/her or by anyone else that might need them.
Back to—OH GOD. CLEAN THIS PLACE UP!! GEEZ...I can't even FIND the BACK BUTTON in this GARBAGE!!