Old joke: Conspiracy theorist Ted Tinfoil dies and goes to heaven and gets to meet God. God welcomes Ted to the afterlife and asks if he has any questions. Ted wants to know who killed JFK. God says "it was Lee Harvey Oswald, acting alone". Ted says "oh no, the cover-up goes all the way to the top!".
Ask Bruce Ivins. (Or, well... you can't...) Five people died from the 2001 anthrax attacks, but they could never find a perpetrator. The prominent people didn't die, but they came close to being exposed.
Bruce Ivins was railroaded by Robert fucking Meuller no less until he committed suicide and years later it would be proven, without a shadow of a doubt I might add, that the facility Ivins worked in did not have the capability to produce anthrax as pure as that used in the attacks.
When it's high profile, they will find someone to pin it on. It's anyone's guess if that person is the actual culprit or just someone that the cops thought they could pin it on.
A salient point and having lived through that period and remember how shithouse panicked everyone was about the anthrax attacks because of how quickly they followed 9/11 (just a week later), I can see there being a lot of impetus for them to find someone, anyone to pin it on so they could calm the US public and make them feel at ease.
Even if the assassin is identified, there will be conspiracy theories and rumors. Now that I think of it, the part with murder and death is completely optional. There will always be conspiracies, as long as the person in question is famous enough.
The first one that comes to mind is Jimmy Hoffa, but they never found the body. He was almost certainly killed by the Mafia, but no specific person was ever prosecuted for it.