Well, it varies in different fanfics. The 11th Doctor could be hurt by powerful villains, or maybe in trying to save someone. It could also be from internal conflicts or emotional stress.
It could be due to various imaginative plot devices created by the fanfiction author. Maybe in a battle with a powerful villain or during a risky adventure.
The story could involve the OC having a special ability or background that complements or contrasts with the 10th Doctor. Maybe it brings a fresh perspective to familiar Doctor Who themes.
One popular character is Charley Pollard. She is a lively and intelligent companion of the 8th Doctor. Another is C'rizz, an alien with his own set of unique abilities and a complex personality.