The Cowboys (6-10) allowed the most points in franchise history (473) and finished 31st in the NFL in run defense this season.
In the team's season-ending loss to the division rival New York Giants, the Cowboys allowed 23 points and gave up 336 total yards to an offense that failed to score more than 19 points in the last five weeks.
"I am appreciative of my relationships with both Mike and Jim, and I am grateful for the contributions that both of them made to our team under difficult circumstances in 2020," Cowboys head coach Mike McCarthy said in a statement Friday. "These are never easy decisions to make, and we wish them, and their families, the very best in the future."
The Cowboys' defense ended the season 23rd in yards per game and 28th in points allowed (29.6). Dallas also gave up 69 plays of 20 or more yards.
If the Cowboys try to replace Nolan with an in-house candidate, George Edwards spent the 2020-21 campaign as a senior defensive assistant. He served as Minnesota Vikings head coach Mike Zimmer's defensive coordinator from 2014-19.