There are three current and often quoted urban legends that started spreading in late 1980s of an ending to the Doraemon series.
* The first and the more optimistic ending was made public by Nobuo Sato several years ago. Doraemon’s battery power ran out, and Nobita was given a choice between replacing the battery inside a frozen Doraemon, which would cause it to reset and lose all memory, or await a competent robotics technician who would be able to resurrect the cat-robot one day. Nobita swore that very day to work hard in school, graduate with honours, and become that robotics technician. He successfully resurrected Doraemon in the future as a robotics professor, became successful as an AI developer, and thus lived happily ever after, thus relieving his progeny of the financial burdens that caused Doraemon to be sent to his space-time in the first place. A dojin manga for this ending was made by a “Tajima T Yasue” in 2005, and it sold 13,000 copies before Shogakukan halted its publication. Tajima apologized to Shogakukan in 2007 and paid an undisclosed amount of money for settlement.. See reference for scans of the ending.
* The second, more pessimistic ending suggests that Nobita Nobi is suffering from autism and that all the characters (including Doraemon) are simply his delusion. The idea that Nobita was a sick and dying little boy who imagined the entire series on his sickbed to help him ease his pain and depression no doubt angered quite a lot of fans. Many Japanese fans staged a protest outside the headquarters of the publisher of the series after learning about this suggestion. The publisher had to issue a public statement that this is not true. (This ending actually correlates to the ending for the series St. Elsewhere, which ended in 1988.)
* The third ending suggests that Nobita fell and hit his head on a rock. He fell into a deep coma, and eventually into a semi-vegetative state. To raise money for an operation to save Nobita, Doraemon sold all the tools and devices in his four-dimensional pocket. However, the operation failed. Doraemon sold all his tools except for one used as a last resort. He used it to enable Nobita to go wherever he wanted, whichever time or era he wished to go. In the end, the very place Nobita wanted to go was heaven.
The plausibility of these issues was discussed here and it was concluded that there is no ending to Doraemon. 
There are three official endings to Doraemon that were made. Doraemon was discontinued in two media because readers were advancing in grades and an ending was believed to be needed. These two are not reprinted.
* In the March 1971 issue of the magazine Shogaku 4-nensei : Due to the fact that visitors from the future were causing too much trouble, the government in the 22nd Century passed a bill to ban time-travelling altogether, meaning Doraemon would have to return to his time era. He leaves Nobita.
* In the March 1972 issue of the magazine Shogaku 4-nensei: Doraemon, for some reason, had to go back to the future but fakes a mechanical problem so that Nobita would let him go. Nobita believes him and promises to wait until Doraemon gets well. Realizing that Nobita can handle his departure, Doraemon tells the truth and Nobita accepts. Doraemon returns to the future.
The third ending was actually meant to be the official ending due to low TV ratings and the Fujiko Fujio duo was busy with other works. But Doraemon did not leave their minds and restarted from next month’s issue. In 1981, this episode was made into anime (called “Doraemon Comes Back”), and in 1998, this was released as an anime movie.
* In the March 1973 issue of the magazine Shogaku 4-nensei, Nobita again returns home after losing a fight against Gian. Doraemon then explains that he has to return. Nobita tries to have Doraemon stay but after talking it over with his parents, he accepts Doraemon’s departure. They take a last walk in the park. After they split up, Nobita encounters Jaian and gets into a fight again. After a long duel with Nobita trying to win at all costs so that Doraemon can leave without worries, Gian lets Nobita win for not giving up. Doraemon finds Nobita passed out and takes him home. Sitting beside sleeping Nobita and after a moment of thought, Doraemon returns to the future. (It is also found at the last chapter of the manga Book 6).
* The animated version is completely similar but lengthened. Nobita finds a box the shape of Doraemon in his drawer. The next day, which happens to be April Fool’s day, Nobita is jeered at by Suneo and Jaian, the latter tricking him about Doraemon’s return. He happily runs home and asked his mother whether Doraemon came back and finds out the truth. Nobita couldn’t stand it and opens the box. Inside of it was a bottle of liquid. He hears Doraemon’s voice explaining that the potion is called Uso 800 (Lies 800) it is used to make all untruths the drinker says true. Nobita uses it to play a few tricks on Jaian and Suneo, like first taking cover then say that the weather sure is good, which becomes a lie and it started to rain heavily before he said it is raining heavily and the rain stopped. Jian and Suneo was scared away after a few tricks and when Nobita mentioned what is happening. Nobita was very happy at first but quickly loses interest in the absence of Doraemon. As he walks home, due to his earlier questioning if Doraemon returned or not, his mother asked him if he could find Doraemon, he unwittingly said, in great disappointment, the truth about Doraemon never coming back, just like what Doraemon told Nobita before his departure. Since the potion was still in effect, when he arrives his room he finds Doraemon there, and they have a happy reunion, but due to the effects of the potion, all his greets and joyful words have to be spoken in the opposite way like I am so unhappy that we can never be together again.. The extended ending from the animated series was eventually adapted to the first story of Book 7 in the manga series, with a few changes (i.e. Instead of hearing Doraemon’s voice explaining the use of the potion, he finds a card inside the box describing the use of the potion).
When the Fujiko Fujio duo broke up in 1987, the very idea of an official ending to the series was never discussed. Since Fujiko F. died in 1996 before any decisions were reached, any “endings” of Doraemon are fan fiction. However, it is apparent from many episodes and movies where Nobita travels to the future that in the end he does marry Shizuka, leads a happy life and separates with Doraemon, although Nobita and his friends fondly remember him.
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