Yume Tsushin is a rather mysterious and surreal game, as expected from a Yume Nikki fangame. Some speculative theories by fans about its hidden narrative are housed on this page.
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Isolation Theory
It is heavily implied in the game that Wormiko is isolated and lonely. This is mostly via her real world Downtown being void of any life and the endings. Both endings feature Wormiko trying to call an unknown person over the phone. In Ending #1 she seems to do so in the Dream World via the Nexus's phone, which shows the phone ringing in another person's bedroom, but no one picks up. In Ending #2 she exits her apartment in the real world and attempts to call someone via a phone booth, but no one picks up again. This may indicate she is not isolated by choice, and she is seeking to get in contact with others. "Tsushin", a part of the game's title, means communication.
Dead Theory
It is possible that Wormiko may be dead.
Wormiko lives on the 4th floor of her apartment. The number 4 is considered highly unlucky in Chinese culture and is often associated with death.
There are many depictions of flesh -- notably rotting flesh -- and body parts in the game. Almost all places Wormiko tries to visit both in the real world and dream world are all abandoned and do not have any life. The boxes in her home housing her belongings instead of them being out on display begs the question if she ever got a chance to truly live in her apartment. Zombie imagery is present in the game, with a zombie effect and the existence of the Zombie Apartment. That may also explain why the lines between reality and her dream world are so blurry and almost indistinguishable to the point where she can bring her hat effect into the "real" world.
A skull is one of the six faces that can be revealed instead of Wormiko’s head during the effect action of the Mascot Costume. Another one of them is an exposed brain with eyeballs.
Not Even Born Theory
It's possible that Wormiko hasn't been born or was even aborted. This theory overlaps heavily with the Dead Theory. There are several instances of egg and flesh imagery in the game, which could relate to her having a Baby effect and an Egg Tart effect. Considering this, maybe some of the fashion effects are showing the life she could've had. You can see cut up body parts on display in one world, and the zombie imagery showing how maybe she yearned to be born in the flesh. This would explain why so many maps are barren and isolated; feeling like she lives on another planet, and she's so far away from others.
In Meat World, a piggy bank can be found broken open and laying on its side. Going inside the piggy bank leads to a small fleshy area with sausages crawling around. It's possible this may be related to the birth imagery in this world, such as the egg NPC that gives the Baby effect.
Zombie Apocalypse Theory
Zombie imagery is present in the game, with a zombie effect and the existence of the Zombie Apartment. The only time humanoid characters try to interact with Wormiko are the zombie people in Zombie Apartment who try to follow her, presumably to infect her too. This could explain why her real world downtown is abandoned. There are many abandoned apartments in her dream worlds, indicating her possible refuge from one affected place to the other. Perhaps she is hiding from the apocalypse and is trying to seek help, explaining why she is trying to communicate on the phone with someone in both endings.
Wormiko’s Father Speculation
The head of the bald man in question.
A head of a bald man with glasses can be seen in Head Space, standing out from the other, more traditional anime-looking heads.
His head is also one of the six faces that can be revealed instead of Wormiko’s head during the effect action of the Mascot Costume.
It is possible that man is (or was) someone close to Wormiko, potentially being a father figure.
Spoilers end here. 
