Warning: for those who have not read the last two books of the Harry Potter series, this post does include spoilers.
Before she wrote Harry Potter and the Deathly Hallows, J.K. Rowling answered a question about the Fidelius charm on her website:
When a Secret-Keeper dies, their secret dies with them, or, to put it another way, the status of their secret will remain as it was at the moment of their death. Everybody in whom they confided will continue to know the hidden information, but nobody else.
Just in case you have forgotten exactly how the Fidelius Charm works, it is
"an immensely complex spell 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" (Harry Potter and the Prisoner of Azkaban)
In other words, a secret (eg, the location of a family in hiding, like the Potters) is enchanted so that it is protected by a single Keeper (in our example, Peter Pettigrew, a.k.a. Wormtail). Thenceforth nobody else - not even the subjects of the secret themselves - can divulge the secret. Even if one of the Potters had been captured, force fed Veritaserum or placed under the Imperius Curse, they would not have been able to give away the whereabouts of the other two. The only people who ever knew their precise location were those whom Wormtail had told directly, but none of them would have been able to pass on the information.
This seemed fine to me when I read it. But then I read Deathly Hallows. Hermione Granger seems to contradict the above explanation. She acts as if everyone in on the secret becomes a Secret-Keeper once the Secret-Keeper dies. If that's right, then the secret can be spread after the Secret-Keeper is dead, and it can be spread by anyone who was told the secret. This is why she thinks the Death Eaters know about Sirius' house once they apparate into its location with a Death Eater in tow. As Secret-Keepers, they can reveal the site to someone.
There's one problem with this. Severus Snape was also in on the secret, and he could have told them the secret. He didn't, and he would have had to have an excuse. If the secret couldn't be told by those who were merely told it, then he would still have that excuse. So is this a sign that Hermione is wrong and Rowling's original explanation is correct? Not necessarily. Perhaps Snape was lying about who the Secret-Keeper was, and Voldemort didn't know it had been Dumbledore. Then Snape would still have an out, and he could pretend not to be able to say. So this isn't really strong evidence that Rowling's original explanation was correct after all.
Some might say that the events of Deathly Hallows confirm what Hermione says. A Death Eater grabs on to them as the apparate within the Fidelius charm's range. Hermione concludes that he's now been let in on the secret, because they as Secret-Keepers brought him there, and therefore he could from that point on tell the other Death Eaters where the house is. It's important to the plot of the book that Hermione at least believe that. Otherwise they'd be able to go back, and much of the book would have gone very differently. But it doesn't actually have to be true. It's certainly possible that they brought him within that range, but I'm not sure he would have become a Secret-Keeper himself because of that, and I'm not sure he would even have been let in on the secret. It's possible the charm would have prevented him from remembering where it was or from getting inside the charm even if he remembered where it was. It's even possible that he died in the process of his body appearing within a Fidelius charm's protection where he's not privy to the secret. We never really find out what happens to him or to the house. Rowling never really addresses that.So I'm not sure which is correct, short of further evidence that I don't remember or didn't notice. It's an interesting question whether to give more credence to the author's own statement (before the last book was written) or a character who's almost always right about this sort of thing (in the last book). This is actually relevant to my piece on destiny in Harry Potter, because one option I'm considering is that Hermione and Professor McGonnagall are simply wrong on time travel, that they've been told something by the Ministry of Magic that isn't true in order to discourage time travel. That would remove the metaphysically impossible suggestions about changing the past while allowing the one time travel story we witness to determine what time travel is like in the Potter universe: you can't change the past but can only fulfill it. But one of the editors of the book thinks it's especially implausible that Hermione and McGonnagall would be wrong on something like that.