Jem's broken arm is definitely a symbol, but of what? An innocent mockingbird with a broken arm is helpless and the ready prey of its predators. Tom, a black man, has a "broken" arm from a life-long injury. We see him in To Kill a Mockingbird when he is helpless and the prey of his predators. Jem is attacked and given a broken arm. This happens after Tom's predator's win in court. Jem's predator was the same as Tom's predator: Bob Ewell. Jem is a white boy. What motivates Bob's attacks? Hatred. He is motivated by the hatred that is fostered by segregation.
So what do these facts add up to? We can start figuring this out by asking what Bob symbolizes. If Bob symbolizes the hatred fostered by segregation, then the broken arm he inflicts on Jem may well symbolize the wound inflicted upon white society by the hate boiling underneath segregation--which we might simplify to the synecdoche "segregation" (i.e., a figure of speech in which the whole refers to a part of the whole; the general refers to the special) and thus say: "Jem's arm symbolizes the wound that the system of segreation inflicted upon white Southerners."
In this symbolism, segregation is presented as a blight that decays and in its dying throes unseeingly attacks in every direction--even in a direction that results in death thrown back upon its practitioners.
My toes touched trousers, a belt buckle, buttons, something I
could not identify, a collar, and a face. A prickly stubble on the
face told me it was not Jem's. I smelled stale whiskey.
"Bob Ewell's lyin' on the ground under that tree down yonder with a kitchen knife stuck up under his ribs. He's dead, ...."
Interestingly, seething hatred of the kind that drives Southern segregation and Bob Ewell, was not the original reason for the segregation that is represented by antebellum slavery. Slavery was an economic function. It was a financial deal. The perpetuation of the economic function required a change of attitude that ultimately resulted in the seething hatred represented in the story by Bob Ewell. The antebellum (i.e., before the war: the Civil War) representation would have been the symbol of an agonizingly captive mockingbird. The post-antebellum (i.e., after the Civil War) symbol is a mockingbird with a broken wing … and a white boy with a broken arm [which, in a way and as an aside, may seem to detract from the import of the mockingbird with a broken wing].