In the Harry Potter franchise, when you know a secret which is held by a Secret Keeper and they die, you yourself become a Secret Keeper in their place.
In Chapter 10 (The Marauder's Map) of The Prisoner of Azkaban on Pages 204-205, Professor Flitwick mentions that being a Secret Keeper imprints this information on your soul:
Well, of course, You-Know-Who wasn’t an easy person to hide from. Dumbledore told them that their best chance was the Fidelius Charm.”
“How does that work?” said Madam Rosmerta, breathless with interest. Professor Flitwick cleared his throat.
“An immensely complex spell,” he said squeakily, “involving the magical concealment of a secret inside a single, living soul. The information is hidden inside the chosen person, or Secret-Keeper, and is henceforth impossible to find — unless, of course, the Secret-Keeper chooses to divulge it. As long as the Secret-Keeper refused to speak, You-Know-Who could search the village where Lily and James were staying for years and never find them, not even if he had his nose pressed against their sitting room window!”
However its unclear how this effects the characters. For example, in The Deathly Hallows Part 2 when the Horcrux stored in the Diadem is destroyed, Voldemort is shown to be aware of it, presumably because part of his soul is being destroyed.
So my question is this: Would someone be aware, in the same manner, that their soul is being altered to contain a secret upon the death of a previous Secret Keeper, or would they actually have to know that this person is dead to realise they've become the secret keeper?