There isn't really a record kept for fewest sacks in a season by a player, as there are thousands of NFL players who have not had any sacks. Michael Strahan holds the record for most sacks in a season, at 22 1/2.
Texas A&M 1991 - 56 sacks
The Chicago Bears hold the NFL team record with 72 sacks in 1984.
Michael Strahan, N.Y. Giants, 2001: 22.5 sacks
"Mean" Joe Greene holds the record for most sacks in a month for the Pittsburgh Steelers.
Michael Strahan, who sacked the QB 22.5 times in 2001.
7 sacks by Derrick Thomas played on Kansas Cheifs