Answer by taking a quote from the following article:

Jean-Christophe Lafaille (31 March 1965 - 27 January 2006 [presumed]) was a French mountaineer noted for a number of difficult ascents in the Alps and Himalaya, and for what has been described as "perhaps the finest self-rescue ever performed in the Himalaya", when he was forced to descend the mile-high south face of Annapurna alone with a broken arm, after his climbing partner had been killed in a fall. He climbed eleven of the fourteen eight-thousand-metre peaks, many of them alone or by previously unclimbed routes, but disappeared during a solo attempt to make the first winter ascent of Makalu, the world's fifth highest mountain.

On the strength of his climbs in the Alps, Lafaille was invited on an expedition to Annapurna by Pierre Beghin, one of the leading French climbers of the day. The pair attempted the mountain's vast South Face following the monsoon season in October 1992 in Alpine style, with no Sherpa support, pre-stocked campsites or fixed ropes on the upper mountain. They had reached a height of 7,400 metres when bad weather forced them to descend. The pair made a series of abseils down the face, but due to their lightweight approach they had little protective equipment and were often forced to abseil from a single anchor to conserve equipment. On the fourth or fifth abseil, Beghin fell to his death when the single cam he was using as an anchor became dislodged from the rock. Beghin had been carrying most of the pair's technical equipment, including all the ropes, and Lafaille was left alone on the face, a vertical mile above safety.  With great difficulty, Lafaille managed to climb down the 75 degree face to the pair's last bivouac site, where he found 20 metres of thin rope, allowing him to make short abseils down some of the hardest parts. With no technical equipment to use as anchors he was forced to entrust his weight to tent pegs or, on one occasion, a plastic bottle. He finally reached what should have been the relative safety of the top of a fixed rope which he and Beghin had installed on a steep rock band, but almost immediately he was struck by a falling rock, which broke his right arm. Disabled and helpless, he lay on a ledge for two days in the hope that other climbers would rescue him. However, while there was a Slovenian team attempting a route on a different part of the South Face, they judged that a rescue attempt would be too dangerous to undertake, so help never came. The cruellest thing about the ordeal, Lafaille said, was being able to see life in the valley below, and by night, the flashbulbs of trekkers' cameras. In spite of this, he later agreed that the Slovenians had made the right decision in not trying to save him.  Eventually, with all hope of rescue gone, Lafaille resolved to continue down alone. He initially tried to continue abseiling, but unable to control the rope with only one hand and his teeth he reverted to downclimbing one-handed, and was utterly exhausted when he reached the Slovenian team's base camp. By that time the climbers at the base of the mountain had given up hope for him, and his first wife, Veronique, had already been told that he had died. Reinhold Messner later said that the survival instinct he showed was of the sort which defines the best mountaineers.

what happened to him
On the fourth or fifth abseil, Beghin fell to his death when the single cam he was using as an anchor became dislodged from the rock.