OK, I'm glad we've reached consensus on this point at least!Right. So there doesn't need to be such action declaration in a mechanical sense
but one must be possible in a sense that fictional events of the characters looking in the safe and finding it empty can occur. Which I also feel is in many genres pretty dramatically reasonable thing to happen, either as a setup for finding the real location, or as a revelation that the characters were fooled. (Perhaps the latter in not something that usually happens in DitV; I don't know.)
Subject to the possibility that I posted about above - of the players putting the location of the dirt at stake, and then losing - I don't think this sort of thing is part of DitV play. Nothing in the rulebook suggests it. The core principle is to actively reveal so as to drive play towards conflict.I tend to look at these things from a fairly cinematic point of view. The characters are at an impasse, they have no dirt. They looked in the safe, nothing was there. What would happen now? Obviously, in a fairly action-oriented genre, there would be some kind of reveal. Some NPC would show up, or another clue would be discovered pointing at the REAL location of the dirt.
In an RPG scenario the first part would simply be explication on the part of the GM. The players would be directing their PCs to find the dirt, and the GM would allow that, having searched the Mayor's safe and not having found it, they encounter the Secretary, who reveals that the dirt is in the keeping of the Mine Owner, and probably some other new plot elements are developed to explain that and likely to add pressure on the characters to act on the information, etc.
So, if the players lose some crucial conflict it makes sense that the mayor might take the papers from the safe and flee with them into the hills. And the GM might even, if they want to rub the players' nose in their loss, narrate them rushing to the mayor's office to find the safe open, and see that the mayor's horse is no longer tethered to the hitching rail outside.
What you describe, @AbdulAlhazred, seems to me more apt in a low/no myth game with an investigation component: the players have their PCs look in the safe buth then fail, and hence instead of finding the dirt they hoped for, the GM narrates a twist or complication: they have to deal with the new NPC, go elsewhere etc.