The sports player case depends on whether the injury is real or exaggerated. Ignoring real injuries could be termed stupid, or carrying on "gung ho"
Urban dictionary: gung ho, mandarin g0nghé .. soldier slang from 1940's meaning to be psyched out for war.
Note if the injury is faked, the sports player could be described as "taking a dive", meaning to try and lose deliberately, or to be "going for an oscar" meaning to act out a facade in the hope of getting positive referee intervention.
A word that comes to mind for the case of focusing on a disability in hope of reward is victim, used in contexts such as in "always playing the victim" or "playing the victim card". There's a great quote from the movie "Adams Family Values" after Amanda volunteers to take part in a life saving demonstration:
Amanda: I'll be the victim!
Wednesday: All your life.
You could also use the phrase "to milk something for all it's worth" in the context of a questionable display of weaknesses.
For single word answers on opposides of the spectrum I would suggest "gung ho" and "victim".