This theory posits that the kids who inhabit the Cul-de-sac are actually dead in reality and that the lives they lead there actually take place in a purgatory-like setting.
According to the theory, the children of the cul-de-sac each hail from different eras spanning the early 1900s to the early 2000s. This would explain why the year for the show is very hard to pinpoint, with multiple anachronisms present, and also why there aren't any adults in the show (although you do catch a glimpse of one every now and then).
Rolf arrived first from the 1900s, the theory goes. His family had moved to Peach Creek in order to establish a farm on its land. Rolf died around 1903 when his family's farm animals stampeded and trampled him. This was the supposed reason as to why he only has one cow, one goat, a few pigs, and a few chickens (not enough animals to cause a fatal stampede) in the afterlife.
Johnny 2x4 came to the Cul-de-sac not too long after Rolf's death. Having no friends, Johnny took a marker and drew a face on a piece of wood, and dubbed it Plank. He died in 1922 after fighting a long battle with tuberculosis, 6 years before the discovery of penicillin. He took his friend, Plank, with him in the afterlife since he was the last thing that he saw in life before he died. Purgatory would also explain Plank's occasional sentient behavior, which is most notably demonstrated in the movie.
Eddy came next. He was born in New York but eventually moved to Peach Creek during the Great Depression era. Always trying to get a quick buck, he always set up scams to get money from the Cul-de-sac kids in an effort to escape the poverty he spent his whole life in. Eddy didn't have a proper father figure since his real father abandoned him and his mother shortly after he was born. With this, came the big bro he adored and idolized so very much despite the latter's abusive nature. After one of his scams went awry, Eddy was chased by the swindled children of the Cul-de-sac, and ran to the lake and jumped into it. Eddy ended up drowning in that lake, and he soon joined the other deceased children in the afterlife. Even though he was no longer alive, Eddy still tried to chase after the "Almighty dollar" by continuing his swindling nature in the afterlife.
Ed and Sarah were the next to arrive at the Cul-de-sac. Their father had died fighting in WWII, and as a result, their mother became distant and disconnected. To cope, Sarah developed her bossy attitude, trying to fill the role their parents used to fill before their father died and their mother stopped caring. Conversely, Ed shut the world out and delved into the fantasy worlds of comic books and monster movies, which exploded in popularity during and after WWII, in order to escape his unhappy life. They both died in a freak car accident in 1953, thus joining the past kids in death.
Nazz was born in the 1960s era to hippie parents. Described as a flower child, she was a rather flirtatious young girl who would always act that way towards the male children of the neighborhood. In the summer of '79, a serial killer escaped from a local asylum made his way into her house and raped and murdered her along with her entire family.
Edd/Double D was born in the 70s when preparing to attend college from a young age became the societal norm expectation, and was raised by very strict, controlling, emotionally distant parents. They pushed him to succeed academically and to be perfectly clean and neat. He is believed to have died as a result of a gas leak causing an explosion with the Bunsen burner from his chemistry set.
Kevin was born around the early 1980s. He was born to a broken-down house, and he also had an abusive father who was poorly-educated and his mother had passed away when he was a year old. Because of his situation at home, Kevin would act his frustration out on the other children of the Cul-de-sac, becoming a bully to cope with his repressed anger. His fascination with his bike fits right in with the birth of the popular X-Games in 1995. One night in the winter of '99, his father fatally beat him in a fit of drunken rage, and he died while he was on his way to the hospital. His father was then convicted of his murder, and he was sentenced to life in prison. When Kevin entered into the afterlife, he re-imagined his father as loving and that he would shower him in gifts. He still kept his bullying ways in the afterlife, however.
Jimmy was the last child to enter into the Cul-de-sac. He was born in the early 1990s, and was diagnosed with leukemia. He never associated with the other Cul-de-sac children, because his parents believed he was too frail to be around the other kids, and he remained bed-ridden for the remainder of his life because of this fact. After fighting a difficult battle with his leukemia, Jimmy eventually succumbed to his illness, and soon the Cul-de-sac Purgatory was complete.
The Kankers were different from the other neighborhood children. It is believed that they are actually demons that were sent to the Cul-de-sac to torment the souls of the remaining children who didn't cross over to Heaven. The Kankers are the only characters with normal-colored tongues, which would seem to indicate that they are not dead, and that therefore, they must be something different. Surprisingly, the Kankers are attracted to the Eds for unknown reasons. However, one common guess is that they are the weakest-willed children of the Cul-de-sac, or because they each symbolize a certain Deadly Sin.