I personally don't believe he truly died. In the beginning of the 12 second flashback, you see their car crash, and it's sudden stop could've cause him to hit his head on the steering wheel, cutting him and start the bleeding. He doesn't get shot by the police Mr. White kills during the scene, because they didn't have time to reach for their guns, they we're shot up fairly fast.
Mr. Orange is distracted by the one-sided gun fight, and the anxiety of the heist, mixed with the fear of being blind and the pain from the hypothetical cut could've made Brown faint, as no one checks his pulse.
My backing up for this is Pulp Fiction. Jimmy is played by Quentin Tarantino, and they are in the same universe and city (Mr. Blonde is Vic Vega, Vincent Vega's brother, Los Angeles)so everyone but he and Mr. Pink die, which could've made Jimmy/Mr. Brown quit his life of crime and get married to Bonnie. It would explain why Jules knows Jimmy, and why Jimmy doesn't want anything to do with Marvin's dead body, because he doesn't want crime in his life anymore.
It would ALSO explain why Jimmy/Mr. Brown says Bonnie would divorce him rather than call the police, because Bonnie knows that he could be charge so much more than Aiding & Abetting, including Mafia Affiliation and Heist. She doesn't want Jimmy/Mr. Brown to be locked up for life, but she also doesn't want to be married to someone who lied about giving up a life a crime for her.
But that's just a theory, so I guess the only one who will know is Quentin Tarantino.