In the comics, Eugene isn't captured by Negan. The storylines don't include such an event. Maybe you got it confused with some other plotlines or characters.
Well, Negan's death in the TWD comics is a result of multiple factors. There's a final confrontation where his enemies unite against him, and he's just outnumbered and outmatched.
In many TWD OC (Original Character) fanfics, Negan's overconfidence could be seen as a weakness. His cocky attitude might make him underestimate his opponents, especially new and unpredictable OCs. This could lead to him making tactical mistakes in battles or negotiations.
Yes, there are likely some out there. You can try searching on fanfic websites like Archive of Our Own (AO3) or Fanfiction.net. Just type in the relevant keywords and see what pops up.
Being saved from Negan is a big deal because Negan was a major threat in The Walking Dead. His brutality and power made him a feared character. So in the fanfic, it could be a turning point for 'them', a chance for new beginnings or a way to show their resilience.