While her tragically iconic suit has been preserved for posterity, the hat has disappeared.
The pink suit itself — famously, horribly immortalized on television — is in a Maryland vault, respectfully barred from public view for 100 years. People now believe Mrs. Kennedy's mother sent it to the National Archive. It was never cleaned, a tacit bow to the First Lady's refusal to change before appearing on TV: "No, let them see what they've done."
But historians have started to wonder what happened to that other grim sartorial icon, the matching hat. Says the LA Times, "The pillbox hat - removed at Parkland Hospital while Mrs. Kennedy waited for doctors to confirm what she already knew - is lost, last known to be in the hands of her personal secretary, who won't discuss its whereabouts." Legally, it's the property of Caroline Kennedy, and it's she who stipulated the hundred years of non-display of the suit.
The fact that clearly Kennedy feels strongly about preserving the privacy of the suit and what it represents seems like the best reason to find the hat. Not that we, out of lurid interest, deserve to ogle it, but that her daughter has a right to prevent exactly that; even icons have owners.