The Near Death Star was a dystopian realm in Futurama as well as the headquarters of the Sunset Squad Robots, who acted as the antagonists of the episode it appeared in - they are all parodies of Star Wars, with the Near Death Star obviously playing the role of the more famous Death Star.
The Near Death Star was a planet covered in spikes, and appeared to be made out of metal. The Near Death Star was inhabited by the Sunset Squad Robots, which were a group of robots that abducted old people past the age of 160.
Professor Hubert J. Farnsworth received word from Mars University that they were revoking his professorship. When he arrived before the university's professors, he revealed all their secrets until he realized it was his 150th birthday party. After everyone talked about how great he is, Farnsworth became concerned with his own mortality. He decided he needed to name a successor. The Planet Express crew expected one of them would be named, including Philip J. Fry, but Farnsworth revealed that his successor would be a 12-year old clone of himself, Cubert J. Farnsworth.
Cubert decided that being an inventor was not an appealing career choice and made cutting and vituperative remarks about the Professor and his inventions. A depressed professor made a recording telling his crew that he had been lying about his age. He was actually 160, the age when robots from the Sunset Squad take people away, never to be seen again. Under cover of an overly-dramatic thunderstorm, a hooded robot arrived and took the Professor away while he was saying good-bye to every inanimate object around him.
The crew set off to rescue the professor and found the Near Death Star, the Sunset Squad's base of operations. The crew sneaked in with Fry dressed up as the professor with Cubert on his back posing as a hump to make him look 'old'. They even brought a huge jar of Cubert's blood just in case. They located the professor, who was unconscious and hooked to a life-support system. They tried to carefully disconnect him, only for the robots discover the crew, forcing them to rip him off and they raced back to the Planet Express ship, Professor Farnsworth in tow.
As they reached the landing pad, Cubert was knocked unconscious, but they made it onto the ship in one piece. When the ship took off, the robots opened fire, damaging the engines. Hoping the Professor would help fix them, they tried everything to wake him up. A reawakened Cubert announced that he knew how to fix the engines and the crew made their escape. (The dark matter engines didn't move the ship, but instead move the universe, allowing the ship to go faster than the speed of light.) Safely back on Earth, Cubert told the Professor that he had decided to follow in his footsteps. The Professor described his experience on the Near Death Star, as he was hooked up to a virtual reality where he had to do everything an old person would do.