The first human who fell down to the Underground survived the sickness they had, but a few years later the two children's parents died a tragic death by another human child.
Their son Asriel swore he would free every monster from the Underground as the new king and would get his revenge on humanity for their deeds.
His sibling Chara feared the humans would be too strong against the monsters and would destroy the monster nation. They told Asriel they would not be part of that crazy plan, moving to the Catacombs and becoming the young caretaker of the old Dungeon.
Meanwhile, their brother Asriel chose Sans and Papyrus as the leaders of the Royal Guard. Papyrus leads the west front, while Sans leads the East.
Meanwhile, after Undyne and Alphys moved to Raindin, Papyrus decided to train Undyne and one day she'll become a member of the Royal Guard.
The Royal Scientist Gaster built an entertaining robot star named 'Madbot'. He got the name from being always upset and irascible, but they still became good friends.
What will happen to these monsters in the future depends on what will Frisk do after they fall down.