Little is known about Tyrell's life before or as the outbreak began, other than that he owned some sort of shop in downtown King County, Georgia. And that he had a license for a shotgun and two handguns, issued to him by Rick Grimes.
Tyrell is mentioned by Rick when he, his son Carl, and Michonne go to King County, Georgia on a run to get guns. Rick remembers that he signed a license to Tyrell for a shotgun and two handguns to keep in his shop before the outbreak, so they head there in hopes of finding his weapons.
It is unknown what happened to Tyrell Debbs after the apocalypse began, leaving her with an unknown fate.