After a deadly disease spreads through the Underground, Alphys is forced to use DT on the entirety of Monsterkind (and even a particular human), creating hundreds of amalgams. Only Flowey is left untouched, as he has a solid body and can't melt.
Shortly afterwards, the world glitches and Gaster is brought back from the void. When he lands back in the Ruins, he runs into America's Favorite Soulless Flower and is determined to go back to his lab in the CORE and find a way to heal the amalgamates (and, if possible, get Flowey a soul in the process).
Gaster: Gaster is the main character of sorts. All current fanfics are written from his POV. He was a successful scientist and the father of Sans and Papyrus, and they lived a happy life until he fell into the CORE. Later, the world glitched and he was brought back into proper existence.
Flowey: Flowey accompanies Gaster through the Underground out of sheer boredom. That is, until he runs into a certain amalgam and suddenly has a reason to care. Not that he actually cares, he just... has a debt to repay.
d͊̃̊̈́͞҉̮͔͉̱̝̭̱̗̀ͅe̩͓̥̺̻͖͉̤ͫ̉t̢̹̘͇̭̩͓͋̇̈̋̃ͭ͂ͅe̷̛̝̜̞̥̮͕̭̠̭̐͂͡r̩̤ͣͩ͟͞͡m̸̹͚͖̮͓ͪ̽̚͠i̠͐̂̆ͤ̕n̐͒ͣ͊̍ͤ̎͏̢͓̤͚͔͘ͅͅa̸̡̩̦̰̫̠̫̭ͯ̋͒ͣ̈́̒̚t̷̡̛̗̥ͯ̌͑ͥͦ͂iͪ̓ͥ͏̠̹̻ó̠̚ͅn̼̥͈͍͗ͫ̽: d͊̃̊̈́͞҉̮͔͉̱̝̭̱̗̀ͅe̩͓̥̺̻͖͉̤ͫ̉t̢̹̘͇̭̩͓͋̇̈̋̃ͭ͂ͅe̷̛̝̜̞̥̮͕̭̠̭̐͂͡r̩̤ͣͩ͟͞͡m̸̹͚͖̮͓ͪ̽̚͠i̠͐̂̆ͤ̕n̐͒ͣ͊̍ͤ̎͏̢͓̤͚͔͘ͅͅa̸̡̩̦̰̫̠̫̭ͯ̋͒ͣ̈́̒̚t̷̡̛̗̥ͯ̌͑ͥͦ͂iͪ̓ͥ͏̠̹̻ó̠̚ͅn̼̥͈͍͗ͫ̽ is the amalgamate of Chara and Frisk. Sit down because you're about to be blasted with some FICTIONAL SCIENCE.
During the Asriel battle, Chara accidentally absorbed part of Frisk's shattered soul. Eventually, the shard grew into a fully formed soul, and they continued to coexist with Frisk. When Alphys injected their body with DT, the two souls were overloaded and melted together. The newly-created soul attracted magic and the dust of dead monsters, creating a seperate body that merged with Frisk's and causing the melted appearance.