Joe and his younger brother, Robbie, were on their own quest in finding a briefcase in the abandoned construction site. After successfully knocking the guard down, Joe and Robbie encountered a slab of concrete, which Joe discovered to be covering a landmine - they also discovered that there was no briefcase to begin with. Joe decided to retreat, but Robbie stubbornly took a landmine, which resulted in his death. It was shown near the end of Downfall that his mother, Mary, committed suicide after Robbie's death and Joe's father blamed Robbie's and Mary's death on Joe, blatantly stating that Robbie had always been the parents' favourite.
Years later Joe got married to Ivy, however due to his 'abuse' as a kid his mentality has started to deteriorate. He got consulted with a shrink, Dr. Frank Zellmann (Dr. Z). However during this time his relationship with Ivy got weakened to the point where they had a divorce which deteriorated his mentality even further, as a result he tied up Ivy and kept her locked up in the cellar of his apartment complex using some type of machine to 'save' her from anorexia and force feeding her. Joe put a hole in his floor as a shortcut to the cellar (which appears in The Cat Lady, going to the flat below Joe's). During this time, Dr. Z sends Joe a message (which you can read in The Cat Lady if you get Mitzi to open up the mailbox) However Joe never checked his mail. Joe tries to bake a cake but realizes he doesn't have sugar. This was after Susan and Mitzi checked his laptop in his flat. He realizes he actually did have sugar the whole time, going back to the apartment to bake a cake for Ivy. Later, Joe checked his answering machine sometime in the future on Friday sent by Dr. Z, which caused Joe to go to Dr. Z. Dr. Z possibly ticked Joe off which rsulted in Dr. Z getting his head bashed into the window before getting mutilated and Joe taking his brain as a trophy. After this, Joe went back to the apartment and killed everyone there (possibly even Susan) and went back to the cellar. Later, Billy and Darren show up to the scene and after some investigating find Joe in a hidden room in the cellar, and Billy tries convincing Joe to stop what he's doing. Every ending ends in the same scenario; Joe and Ivy escape, and Joe states they're going to a 'small country hotel'. Arriving at the hotel is actually the start of the game. Which means gameplay wise - the game is a big loop.
There are some references to Downfall in The Cat Lady. A list of these references can be seen below.
In The Cat Lady, after being caught by Joe in his apartment, the player can choose Susan to say that she's a gas inspector and was inspecting his apartment for a gas leak - this is a reference to one of the puzzle in Downfall where the player has to turn on the gas for the gas stove in the 4th floor bathroom by pulling a lever in the basement.
In The Cat Lady, there is a black cat satatue in Joe's flat that can be seen from flat 1 through a hole in the floor. Susan has to get the statue and break it in order to retrieve the key to Joe's flat - in Downfall, Joe actually has to kill a Black Cat in order to retrieve the key for room 402. The Black Cat is actually Joe's mental recreation of the cat by the same name owned by him and Ivy, however it shows in a dream that Lucifer swallowed a bunch of needles and Joe drowned him to save him from pain - and at the end of Downfall it shows a black cat with its stomach cut open smushed onto the wall. This is possibly Lucifer who Joe tried to save by cutting his stomach open to retrieve the needles. It is also inforced that Joe and Ivy own a cat when Susan makes note of this when she and Mitzi are creating a map for the apartments.
In The Cat Lady, whiled creating a map for the apartments, Susan satates that Joe and Ivy live across the hall, but then quickly comments she thinks Ivy's name is probably Sophie. Which is a reference to the antogonist of the same name in Downfall.