Looks like all 300 are on the rock at the same time in this picture.
After the cables go up for the season (usually just before Memorial Day), an additional 50 Half Dome permits are released each day.
Man falls of Half Dome (August 23, 2011) Climbers near the base of Half Dome reported seeing a man drop down the 2,000 face. A male body was found in the talus slopes on the Mirror Lake side of Half Dome known as the Death Slabs.
Fatal Fall From Half Dome Cables (April 19, 2007) Jennie Bettles, a 43, from Oakland, California slipped off the Half Dome cables and slid out of sight. The cables are laid down on the rock this time of year and the stanchions which hold the cables up are removed to prevent damage by avalanches. Rescue personnel began hiking up the nine trail miles toward Half Dome because weather made flying impossible. The team was turned around above the shoulder of the dome several hours later by heavy snow, wind, and icy conditions that made travel on the exposed ridge too dangerous even before they reached the bottom of the cables. The bad weather continued throughout the following day and the dome was never out of the clouds. The weather broke the following morning and a spotter posted across Tenaya Canyon from Half Dome picked out what he believed was a body in the gully to the north of and below the cables. The location of the body, about 1,000 feet below the base of the cables, was confirmed from a helicopter. A recovery team was flown to the shoulder of Half Dome and was able to descend to the victim utilizing crampons, ice axes and roped climbing. The body was flown out by long line under a helicopter.