It is unknown if any civilians live in this realm and it may just be a military dictatorship.
Nothing is known of the history of this realm or what happened to spur the Subspace war, but it is possible that a power hungry Tabuu just got greedy and wanted to take over the World of Trophies.
The first instance of Subspace in the world of trophies was at the Midair stadium after a scheduled match between Mario and Kirby, when a Subspace Bomb was detonated in the stadium. Throughout the course of the war many other locations succumbed to the subspace bombs, including Castle Dedede, The Ruins, and the Floating Island of the Ancients.
After the events of the isle (where all remaining bombs were detonated to open a hole for the Subspace Gunship) and the failed attempt at using The Subspace Gunship, the fighters then used this portal to enter the subspace realm. There they learned that Tabuu was taking the bits of their world to create the Great Maze. The fighters then fought and killed Tabuu, causing all the locations ( with the exception of the isle) to be restored.
It is unknown what happened to the realm after Tabuu's death but it is possible it was destroyed.
There are only two known ways to enter the subspace from outside at this time: one is to use a subspace bomb and the other is the subspace gunship. however following the death's of all R.O.Bs and the destruction of the gunship it is posssible that the realm my no longer be accesed