Symbolism, Imagery, Allegory
The photo of Clementis and Gottwald is literally the first thing we see in this novel. Clementis offers Gottwald his hat to keep the chill away. It's a Kodak moment. But after Clementis is executed as a traitor, the propaganda boys do away with the image of Clementis on the balcony—they literally take him right out of the photo—but they forget about the hat.
So, Clementis is still in the picture. His hat is like a secondary relic of a saint, a reminder that his presence was real. For Kundera, the Hat That Wouldn't Die becomes a symbol of resistance, a thumbing of the nose at the attempts of the Communists to blot out people and events. He brings up the hat again when Mirek is about to be hauled away:
They wanted to efface thousands of lives from memory and leave nothing but an unstained age of unstained idyll. But Mirek is going to land his small body on that idyll, like a stain. He'll stay there just as Clementis's hat stayed on Gottwald's head. (I.19.4)
It doesn't even matter that Clementis' hat probably never was on Gottwald's head. For Kundera, it's a bit of revisionist history that keeps him going.