The fallacy of negative proof occurs when the lack of evidence for something is taken to justify the conclusion that it did not exist. The logical error involved becomes obvious when shown as a syllogism:
P1: No evidence has so far been found for A;
C: Therefore A did not exist/happen.
This is a formal fallacy: what is needed is an additional premise, to the effect that no evidence for A will ever be found subsequently.
A good example of this fallacy is found in studies of historical figures or events, especially religious ones, such as the debate over the historicity of Jesus or the existence of Atlantis. Where a person is referred to in stories or sagas, say, but no other evidence of their actual existence is found, should we conclude that the person is fictional? Notice that there is a considerable difference between claiming that the lack of evidence proves that the person did not exist (i.e., the negative proof fallacy) and asserting that the likelihood of their historicity is small; however, an elaboration of how such probabilities are assigned is still required.
Paul Newall, "The Logical Fallacies of the Historian" in A Companion to the Philosophy of History and Historiography (Blackwell Companions to Philosophy), pp.270-1.