Selected by the Raiders in the fourth round (106th overall) of the 2019 NFL Draft, April 27, 2019. Crosby was born in Michigan but his family moved to Texas when he was in middle school. He was an All-Area pick as a senior at Colleyville Heritage High School before coming back to the state of his birth to play with the Eagles. Crosby was the squad's Defensive Scout Team Player of the Year during his redshirt season in 2015. He played in all 13 games as a reserve the following season (35 tackles, 5.5 for loss, 1.5 sacks). Crosby broke out as a sophomore, earning first-team All-MAC and team Most Valuable Defensive Player honors after starting all 12 games and compiling 57 tackles, 16.5 for loss, and a team-high 11 sacks and four forced fumbles. MAC coaches voted him first-team all-conference in 2018, as well, rewarding him for his 70 tackles, 19 for loss, 7.5 sacks, four pass breakups, and four forced fumbles in 12 starts.