Manipulation. It could be a way to manipulate Snape further. If Snape feels cared for, he might be more likely to do whatever Voldemort asks without question. Voldemort is a master of manipulation, and this could be just another tactic in his arsenal.
Power. Voldemort might see Snape as a means to gain more power. Snape is highly intelligent and skilled in the Dark Arts. By caring for him, Voldemort could be ensuring that Snape remains loyal and continues to use his skills for Voldemort's benefit.
Perhaps a sense of kinship. In some fanfictions, they might explore the idea that Voldemort, in his own dark and twisted way, sees something of himself in Snape. They both have a connection to the Dark Arts and a certain level of isolation, and this could lead to Voldemort caring for Snape in a strange, dysfunctional way.
In some fanfictions, Snape might be working with Voldemort because he has been blackmailed. Voldemort could have found out some deep, dark secret about Snape and is forcing him to cooperate. This could be related to Snape's past or something he has done that he doesn't want to be made public.
One possible motive could be his love for Harry's mother, Lily. Even in the fanfiction, this could be a driving force. He might see helping Harry as a way to atone for his past actions towards Harry.
There could also be a plotline where Hermione discovers some of Snape's past traumas and in trying to help him, they form a bond. Snape, out of gratitude and a newfound respect for her, starts to take care of her like a mentor. He shields her from the harsh judgments of other Hogwarts professors and students alike, and together they work towards a better future for the wizarding world.
One possible plotline could be that Snape discovers a hidden weakness of Voldemort. Maybe through his years of spying, he finds out that a certain spell, when combined with an ancient magic artifact, can destroy Voldemort. So he devises a plan to get hold of the artifact and uses the spell at a crucial moment when Voldemort is off - guard, perhaps during a major battle when Voldemort is focused on other opponents.
A really interesting plot twist could be that Snape discovers a new form of magic. Since he's not involved with Voldemort's dark arts, he has more time and mental energy to explore other areas of magic. Maybe he stumbles upon a long - lost magic that can counteract the most powerful dark curses. This discovery could change the balance of power in the wizarding world, making it so that Voldemort's rise is not as inevitable as it seemed in the original story.
One possible motive could be jealousy. Snape might be really good at certain subjects like potions, and the Marauders, being competitive, might bully him to make themselves feel better.
Differing ideologies during the wizarding war. If James was seen as a threat to Snape's side (even if Snape was on the wrong side, from a moral perspective), Snape could justify killing him. For example, if James was too aggressive in fighting the Death Eaters and Snape thought it would lead to more bloodshed, he might take matters into his own hands to stop James.
Well, in this sort of fanfiction, Ginny's motive could be a complex web of emotions. She might be under the influence of a dark spell. Or perhaps she has been misinformed about Harry's role and believes that by giving him to Voldemort, she's actually saving the wizarding world. It could also be a case of extreme jealousy, if the writer wants to explore a really twisted version of her character.
There's a fanfic where Snape takes advantage of a power struggle within Voldemort's ranks. He poisons Voldemort's drink during a meeting, which causes Voldemort to become severely ill, an injury in a sense. Snape does this to try and disrupt Voldemort's plans and give the Order of the Phoenix more time to prepare their defenses.
Yes, it could be possible in fanfiction. Fanfiction allows for wild reinterpretations of the source material. Maybe there could be a story where a dark wizard in the past manipulated their family trees so that Harry, Snape and Voldemort are unknowingly brothers. It would make for a very interesting plot, full of drama and conflict as they are on different sides in the original story.