One possible plot could be that in a dark, alternate universe, Frisk accidentally wanders into a powerful monster's lair. The monster, feeling threatened by Frisk's presence, attacks without hesitation. Frisk, being human and relatively defenseless, is quickly overpowered and killed. Another plot might involve a betrayal within a group of friends. One of Frisk's so - called friends becomes envious of Frisk's popularity or kindness and devises a plan to get rid of them. They set up a situation where Frisk is in great danger and ultimately meets their demise. A third plot could be related to a curse. Frisk unknowingly breaks an ancient curse that was placed on the land, and as a result, the curse takes their life in a rather cruel and unexpected way.
When Frisk gets killed in a fanfiction, it usually creates a very somber and dark mood. Frisk is often a character associated with hope and new beginnings, so their death is like snuffing out that light. It can make the story feel more tragic and hopeless, as if all the good that Frisk could have brought has been lost.
Toriel is very likely to be involved. She has a motherly nature and would surely be concerned about Frisk's health. She would probably be at Frisk's bedside, offering comfort and warm food.
Often, there's a plot where the sickness is some sort of mysterious ailment that no one really understands at first. So, the characters like Sans or Papyrus might try to use their own unique ways to figure out what's wrong with Frisk. Papyrus could try to 'doctor' Frisk up with his 'amazing' but not always accurate medical knowledge.
It could be some of the more aggressive monster characters. For example, the dog monsters might be territorial and see Frisk as an intruder, so they bully Frisk.
Well, it could be that in this fanfiction, Frisk gets bullied because they come from a different background than the others. The bullies target Frisk for being an outsider. As the story progresses, Frisk could meet a mentor - like character who helps them gain confidence and teaches them how to deal with the bullies. Frisk might then use kindness and understanding to turn the situation around and make the bullies realize their mistakes.
One common theme is the exploration of the emotional aftermath. Characters around Frisk might experience shock, grief, or guilt. For example, if Sans is in the story, he could be filled with rage at the situation and vow revenge. Another theme could be the struggle for survival if Frisk doesn't die immediately. They might have to fight against their own fading life force while also dealing with the threat that led to them being shot in the first place. Also, there can be themes of redemption if the one who shot Frisk has a change of heart later in the story.
Asgore would be deeply affected. He has a complex relationship with Frisk, but ultimately he doesn't want harm to come to them. His reaction could be one of shock and regret. He might see this as a sign that his rule over the Underground has failed in some way. Flowey, depending on his state of mind in the fanfiction, could also have a strong reaction. If he has any positive feelings towards Frisk left, he'd be either very sad or extremely angry, and might try to manipulate the situation to his advantage.