Fascist Earth was the name given to an illusion created by a group hallucination experienced by the Dwarfers.
When the Despair Squid attacked Starbug with its venom, the Dwarfers awoke to find themselves in a TIV Game suite. The attendant told them they had been playing Red Dwarf for four years and that their memories would return shortly.
As they explored their new identities, the Dwarfers learned that they were very different from the people they remembered themselves to be. They decided to leave the arcade and discover more.
As they left, they read a series of posters which told them about the policies of the government of their new home. More information was later provided by a police officer whom they encountered while he was pursuing a small child for stealing an apple.The government was a totalitarian regime which oppressed the people with harsh policies. They had been in power for at least 20 years and rewarded citizens for betraying each other to the authorities.
The police were heavily armed with firearms and personal rocket launchers, and enjoyed broad powers to kill suspects without trial. Lister was dismayed to discover that he was really Colonel Sebastian Doyle, Head of the Ministry of Alteration. The Ministry was an assassination bureau that "purified" democracy by killing people who opposed the government.
Kryten was forced to shoot the policeman to save the child, so that the Dwarfers had to go on the run. Escaping from motorcycle troops and a helicopter, they all decided to commit suicide rather than live as the people they appeared to be in this reality. Fortunately, Holly was able to convince Kryten to release a mood stabiliser into the air, which broke the hallucination and brought them back to reality (RD: Back To Reality).
Although this was only a hallucination, dimension theory states that this reality continued to exist in an alternative, parallel dimension.