Do you want this for a story you are writing?  A lot depends on
time scale -- do you want the victim to get in trouble days,
weeks, months or years after injury?

Tetanus.  Rabies.  A minor wound contaminated with somebody else's
blood could result in AIDS, hepatitis or other blood-borne disease.

A very small penetrating wound of the body cavity could result in
a fatal infection.  If you need to delay the result, I suppose a
wound that didn't quite penetrate could abscess and later open into
the abdomen causing a fatal peritonitis.

A small crack in the base of the skull can leak cerebrospinal fluid
into the back of the throat.  If bacteria manage to make the reverse
trip, the person can develop a serious infection of the brain.

I suppose an injury that damaged but didn't penetrate a major blood
vessel could leave a weak spot that might later rupture.

I'm not a doctor -- most of this is handwaving.  If any of it is
absurd, I hope the more knowledgable will correct me.