In this fanfiction, the afterlife might be a place where Snape can finally be free from his past burdens. Hedwig could be a symbol of purity and freedom. She might help Snape come to terms with his complex feelings towards Harry Potter and his role in the wizarding world. For example, she could lead him to see how his actions, although often misunderstood, had a positive impact on the overall battle against Voldemort.
It could be a story where Hedwig serves as a sort of guide for Snape in the afterlife. Maybe she shows him the good he did that was overlooked in life.
Perhaps in this fanfiction, Hedwig and Snape form an unlikely friendship in the afterlife. Snape, who was often alone in life, finally finds some peace with Hedwig's company. Hedwig, being a magical creature, could have unique insights into the afterlife that she shares with Snape.
One plotline could be that Snape is initially confused in the afterlife and Hedwig appears to him, bringing a sense of calm. They start to communicate in a way that was not possible in life.
One possibility is that in the afterlife, Snape finally finds peace. He no longer has to hide his true loyalties or endure the scorn of those who misjudged him. He might be reunited with Lily, and they could have the conversations they never had in life. He could also meet with Dumbledore again, and they could discuss all the secrets and sacrifices that were made during the war.
In this fanfiction, perhaps Snape finally gets the chance to truly apologize to Lily. He might express all the unspoken feelings and regrets he had when she was alive.
In the afterlife, their relationship could be one of healing. Regulus, having made amends for his past mistakes in a way, could finally have an open and honest conversation with Sirius. They might start to understand each other's motives better. Sirius could see that Regulus was always trying to fight the dark forces in his own way, and Regulus could understand Sirius' need for freedom and justice. They could spend time reminiscing about their childhood, both the good and the bad parts, and form a closer bond than they ever had in life.
There could be other Death Eaters that Snape knew in his life. In the afterlife, they might be there to either confront him about his double - agent status or to seek redemption themselves. And sometimes, characters from Snape's childhood, like his parents or childhood friends, might appear to add more depth to his backstory and his experiences in the afterlife.
Perhaps in the fanfiction, Hedwig is lost near King's Cross Station. Snape, who is there for some mysterious reason, decides to help find Hedwig. As he searches, he starts to understand the significance of Hedwig to Harry and through this, his view of Harry softens a bit. It could be a story about unexpected connections and growth in Snape's character.
One interesting idea could be Snape finally getting the recognition he deserved in the afterlife. Maybe he is reunited with Lily and she thanks him for all he did to protect Harry. Another could be that he gets to teach in a magical afterlife school, sharing his vast knowledge of potions and the Dark Arts.
If he meets Lily in the afterlife, their relationship could become more of a true friendship. Without the complications of James Potter and the war, they could finally understand each other on a deeper level. Snape could let go of his unrequited love and instead cherish the bond of friendship that was always there beneath the surface.
In the fanfiction, Hedwig could be carrying a small parcel that she drops near Snape. Snape, out of curiosity, picks it up and discovers it has something to do with Harry. This could lead to a conversation - like interaction where Snape talks to Hedwig as if she can understand, expressing his mixed feelings about Harry. Hedwig could then hoot in response, almost as if she's giving her own opinion.
Snape might be portrayed as a more vulnerable character in this fanfiction. Away from the pressures of the wizarding world, he can show his true emotions to Lily.