Snape could be very cautious in his interactions. He would be constantly aware of the power dynamics. He might flatter the more powerful Death Eaters subtly to avoid suspicion. For instance, he could compliment Bellatrix on her loyalty to the Dark Lord. At the same time, he might try to intimidate the weaker ones to show that he's not to be trifled with. He might use his knowledge of the Dark Arts to his advantage in these interactions, like casually mentioning a difficult spell he's mastered to gain some respect.
He could be suspected by Voldemort. Since Voldemort is very paranoid, an injury at a meeting might make him think Snape is up to something or being careless in a way that could endanger their plans.
There's also the possibility that it was an accident. Fanfiction often plays with the idea of magical accidents. Maybe a spell misfired during a demonstration or a fight that broke out among the Death Eaters that Snape got caught in the middle of, and as a result, he got injured.
One possible plot twist could be that Snape is actually there to spy on the Death Eaters for Dumbledore, but the other Death Eaters start to suspect him. Maybe he accidentally reveals some knowledge that only a spy would know. For example, if he knows about a secret mission that was supposed to be only known within the Order of Phoenix. Another twist could be that Snape has a secret agenda of his own that is different from both Dumbledore's and Voldemort's. He might be trying to manipulate the situation within the Death Eater meeting to his own advantage, perhaps to gain some sort of power or information that could be used as a bargaining chip later. And finally, there could be a twist where a new character shows up at the meeting who has some sort of connection to Snape's past, and this changes the dynamics of the meeting completely.
Bellatrix Lestrange is also a likely candidate. Her encounter with Hermione would be extremely intense. Given her loyalty to Voldemort and her rather unhinged nature, she would likely pose a serious threat to Hermione, but Hermione might also find a way to use Bellatrix's madness against her.
Bellatrix Lestrange's younger brother or some other minor Death Eater character could be used. This would allow for the creation of a new character with his own motives and backstory. He could be betrothed to Hermione as part of a larger plot by Voldemort to gain control over Hermione's knowledge and magic. This would put Hermione in a very difficult position as she would be tied to a very dark and dangerous family.
There's also a possibility that it could be a minor Death Eater that we don't know much about from the original series. The author of the fanfiction could create a new character who was a Death Eater but is now having doubts. Hermione could be the one to find this person and start their journey of change. This would give the author a lot of creative freedom to develop the character's backstory and their relationship with Hermione.
It could be someone who has a hidden good side, like Draco Malfoy. He was from a Death Eater family but showed signs of not fully embracing the dark side. Maybe in this fanfiction, he decides to protect Hermione for some unforeseen reason, perhaps because he has developed a new understanding of the value of life and friendship.
One possible motive could be a deep - seated dissatisfaction with the wizarding world's status quo. Maybe she felt that the Ministry of Magic was corrupt and that the Death Eaters had a better vision for change, although a very dark one. Another could be some sort of personal vendetta against someone in the Order of the Phoenix or Hogwarts faculty that made her side with the Death Eaters.
In some fanfictions, Percy Weasley may be depicted as a Death Eater, but this is a departure from the original canon. Fanfiction allows for creative reinterpretations, and some authors might explore this dark turn for his character to add drama and new plotlines.