Boxer's fate is that he dies of wounds that he sustains at the Battle of the Windmill. He might have survived, but Napoleon doesn't really care enough to get him medical help.
Boxer's character traits affect his fate because his main character trait is his unquestioning belief in Napoleon. Boxer is supposed to represent the working classes who blindly followed communism.
Boxer keeps working really hard even after he's wounded and even after his lung collapses. He truly believes that whatever Napoleon says is best so he just keeps on going.
This trust in Napoleon dooms him.
Boxer represents the poor gullible working class people of Communist Russia who worked tirelessly and unquestioningly to oust the Tsar but were eventually betrayed by Stalin and his henchmen who took advantage of their illiteracy-Boxer can remember only the first four letters of the alphabet-and their simple trustworthy nature.
Boxer's gullibility and loyalty to Napoleon are his undoing. He believes everything that Napoleon says - "Napoleon is always right," which of course is a direct take on "Mussolini is always right."
In Ch.9 we read of the tragic death of Boxer the veteran of the "Battle of the Cowshed" and the "Battle of the Windmill." Boxer's motto had always been "I will work harder," and it is precisely this over exertion in rebuilding the windmill which finally results in his death. One day he collapses and is taken away to the slaughterhouse where his body parts are commercially exploited. Squealer manages to convince the other gullible animals by lying to them that Boxer died in spite of the best medical care being given to him. Napoleon also fools the animals by making a speech in honour of Boxer and orders for a large wreath to be placed on his grave.