[Legolas]

Long afterwards, as the Third Age of the Elvish World waned and the War of the Ring approached, it was revealed to the Council of Elrond that the Ring had been found, sunk near the edge of the Gladden Fields and close to the western bank; though no trace of Isildur's body was ever discovered. They ere also then aware that Saruman had been secretly searching in the same region; but though he had not found the Ring (which had long before been carried off), they did not yet know what else he might have discovered.
But King Elessar, when he was crowned in Gondor, began the re-ordering of his realm, and one of his first tasks was the restoration of Orthanc, where he proposed to set up again the palantir recovered from Saruman. Then all the secrets of the tower were searched. [...] At last behind a hidden door that they could not have found or opened had not Elessar had the aid of Gimli the Dwarf a steel closet was revealed. Maybe it had been intended to receive the Ring; but it was almost bare. In a casket on a high shelf two things were laid. One was a small case of gold, attached to a fine chain; it was empty, and bore no letter or token, but beyond all doubt it had once borne the Ring about Isildur's neck. Next to it lay a treasure without price, long mourned as lost for ever: the Elendilmir itself, the white star of Elvish crystal upon a fillet of mithril 31 that had descended from Silmarien to Elendil, and had been taken by him as the token of royalty in the North Kingdom

When it says 'no trace of Isildur's body was ever discovered,' it means that it was never discovered as a result of any searching done by the forces of good (primarily the Council and those in allegiance with Imladris).

The passage continues (and fully explains what happened, I think)...

When men considered this secret hoard more closely, they were dismayed. For it seemed to them that these things, and certainly the Elendilmir, could not have been found, unless they had been upon Isildur's body when he sank; but if that had been in deep water of strong flow they would in time have been swept far away. Therefore Isildur must have fallen not into the deep stream but into shallow water, no more than shoulder-high. Why then, though an Age had passed, were there no traces of his bones? Had Saruman found them, and scorned them – burned them with dishonour in one of his furnaces? If that were so, it was a shameful deed; but not his worst.