Eugene Alvin Broxton was born on February 27, 1955, in Louisiana, United States. 

Eugene Alvin Broxton's crime spree began on June 3, 1986, when he attempted to rob a store and shot at a police officer named Walt Hays while trying to escape. Broxton was caught and received a 13-year sentence. After being paroled in 1990, he developed a serious drug addiction. This addiction led him to commit violent crimes, including murder.

On April 6, 1991, Broxton broke into the home of 46-year-old Gary Wayne Stuckwisch. He stabbed Stuckwisch to death and stole his belongings. Broxton then abandoned the stolen car the next day. Thirteen days later, he kidnapped a man named Gordon John Miller, a 59-year-old TV guide salesman. In view of witnesses, he stabbed Miller to death and fled in his truck.

On May 2, 1991, Broxton was arrested for stealing a radio from Walmart. Though this was a violation of his parole, he was fined instead of sent back to prison due to it being seen as a minor offense. Just four days later, he killed a 64-year-old retiree named Albert Krigger by strangling him and later pawned a ring stolen from the victim.

On May 10, Broxton returned to Walmart and kidnapped 65-year-old Gary Leon Andrews at gunpoint. Broxton drove Andrews to a remote location where he robbed and shot him in the mouth, then stabbed him in the stomach. Despite being seriously injured, Andrews survived.

On May 16, Broxton targeted a motel in Channelview. He pretended to be a motel employee and gained entry to the room of newlyweds Waylon and Sheila Dockens. He bound and gagged them, then shot them with a .44 Magnum. Sheila died from her injuries, while Waylon survived but was critically wounded.

Broxton was arrested two days later. Investigators found his fingerprints at various crime scenes. He was charged with three counts of capital murder and two counts of attempted murder. During the trial, Waylon Dockens identified Broxton as the attacker. He was found guilty of killing Sheila Dockens and was sentenced to death.

Over the years, Broxton tried to appeal his conviction, but his attempts were repeatedly denied. In 2003, he was retried and again sentenced to death. As of February 2024, Eugene Broxton remains on death row at the Allan B. Polunsky Unit, awaiting execution.