Still, it’s a stretch to say that his death defined him. I don’t think it’s true. Cleopatra, another nope. Some of these are just “I remember how this person died.” Not enough.
One who hasn’t been mentioned is Archduke Franz Ferdinand. That one does match this thread.
Ernest Hemingway’s death by suicide at 61 doesn’t define him, of course, but I think it definitely redefined his legacy. He had built up a carefully crafted mythos of a manly adventurer, while behind the scenes he battled depression all his life and self-medicated with alcohol. Mental illness and suicide runs rampant in his family: his father and 3(!) of his siblings all committed suicide, and his granddaughter Margaux later died from ODing on barbiturates.
To be clear, I don’t think that diminishes his legacy at all; if anything I think it deepens his legacy. He did have a heck of a life, battling his demons the way he knew how to. Perhaps if he had gotten therapy early on, and if he had had access to modern medications, perhaps he wouldn’t have felt the need to drink swimming pool-sized quantities of alcohol, and could have had more time to enjoy his twilight years. But then there’s always the question: if he had been happier, would he have been more ordinary?
Heath Ledger’s and River Phoenix’s premature deaths probably fit.
Mata Hari.
Judge Crater
Amelia Earhart
The OP asks for famous people whose death “sort of” defines them, not “absolutely defines” them. Famous people are famous for the things they do before they die. If asking for “absolutely defines” them, I don’t think anyone listed in this thread so far applies. Example: JFK is remembered (by me at least) more for his charisma, the Bay of Pigs, the Cuban Missle Crisis, the Space Race, etc. than his assassination. Jesus did a lot of things (including impressive parlor tricks) before he died, too.
Drug ODs from people in the entertainment industry aren’t that unusual.
Some people are too famous that the standards for their death would need to be really high. Baseball players Lou Gehrig and Roberto Clemente are likely remembered for how they died, but they were big enough stars that it’s not the only thing they should be remembered for.
One that comes to mind is Willard Hershberger. He was a catcher for the Cincinnati Reds, who committed suicide during the 1940 season. He was despondent over mistakes that he felt had cost his team games. The Reds went on to win the World Series that year. Ironically, Hershberger, who was a backup, would have played a lot in that series since the regular catcher Ernie Lombardi wound up getting hurt.
Another is Ernie Davis, a running back from Syracuse. Drafted first by the Washington Redskins, would have been the first black player on the last NFL team to integrate. He was traded to the Browns (for another black player, Bobby Mitchell) but contracted leukemia and died without playing in the NFL.
Caesar’s assassination slightly delayed the transition from Republic to Empire. But that transition was made inevitable by the deeds he did during his life (most notably, crossing the Rubicon with his army).
@Jay_Z 's nomination of Archduke Ferdinand definitely qualifies, though. As a very high-ranking noble, he was definitely famous in life, but nothing he did in life could possibly compare to setting off the powder keg of Europe.
I don’t really know anything about Cliff Burton other than “he was the guy from Metallica who died in a bus crash.”
Also Ronnie Van Zandt of Lynyrd Skynrd. Even though the band was pretty famous, a casual fan would be hard pressed to not describe him as “The guy from Skynyrd…who died.”
Heath Ledger I’d say no, he’s better known as the joker more than he’s known as another star who died young. River Phoenix probably qualifies IMO, he’s better known for the manner of his death than any particular role.
Nope again from me. She’s synonymous with spying, specifically using her sexuality as a means of gathering intelligence, rather than being executed.
Though in that vein, the Rosenbergs probably count.
Leon Trotsky
The OP mentioned famous, and Kitty Genovese was certainly famous, and defined by her death. However, the title of the thread that you didn’t start is “Deaths that sort of define a person”, not famous people who died.
I disagree.
JFK’s assassination is probably what he is MOST remembered for-particularly by younger generations. I know plenty of people who don’t even know what Bay of Pigs or the Cuban Missile Crisis are.
I’d agree with this. To this day, whenever I hear River Phoenix’s name, I think of the Viper Room and him dying on the sidewalk outside of it. Heath Ledger’s death, on the other hand, isn’t as memorable to me. Drug OD? Sure, but it doesn’t define him, or even “sort of” define him, imo.
As the person who originally mentioned Heath Ledger --I can understand your argument.
However I think this points out how subjective this can be particularly among different generations.
Because if I ask my elderly mom about Heath Ledger the only thing she will remember is the media coverage of his death.
And this brings to mind Sharon Tate because the main thing I remember her for is being one of the Manson family’s victims and NOT any of her acting roles. Others may not feel the same way about her.
This one is borderline. I mean at first glance, hell no, Trotsky was a huge figure in Soviet and European history long before he was assassinated. Though counterargument would be how many people a century later actually know that history (or in fact know him as anything other than a line in Stranglers song, though possibly even that reference is aging out 
)
I mentioned her at the top of the thread.
Ray Chapman.
In 1920, while batting for Cleveland in an American League baseball game against the Yankees, he was hit in the head with a pitch. He was able to start walking to the clubhouse before he collapsed.
And to date he is the only person to die while playing a Major League Baseball game.
The problem, it seems, is that we have not defined define or even sort of define, so we can always argue against somebody’s choices. But I think most of the examples given are quite good, and I second Julius Caesar, even if crossing the Rubicon is considered more definig of him as a person. Had he died peacefully in his bed Shakespeare would hardly have written a play about him. But many still would have learned Gallia est omnis divisa in partes tres. Would there still be a comic called Asterix the Gaul?