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.
A possible plotline could be that Severus was framed as a Death Eater. He might be trying to clear his name throughout the fanfiction. Another idea is that he is part of a secret organization that is dedicated to taking down the Death Eaters from the inside, but they have to operate in secrecy so it appears he is one of them.
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.
One way is by emphasizing his true loyalties all along. Maybe he was secretly working against the Death Eaters while pretending to be one. His love for Lily could be the driving force. He could be shown as using his position among the Death Eaters to gather intelligence for the Order of the Phoenix, constantly trying to undermine Voldemort's plans without the other Death Eaters suspecting.
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.
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.
In this type of fanfiction, the relationship between Hermione and the Death Eater could be very complex. Maybe it starts as a hostile one, but as the story progresses, they might find some common ground or mutual understanding. It could also be a story of redemption for the Death Eater through Hermione's influence.