The Bears cannot suspend him, IIRC. The NFL CBA vests the league itself with the right to assess fines and suspensions for this type of issue. This issue was resolved via the Owens and Keyshawn issues of recent years, where TB and Philly tried to get around the rule by placing players on the "inactive list" rather than suspending them or showing them the door. EDIT: BTW, it is illegal in the State of Illnois for an employer to base an adverse employment action on anything short of a criminal conviction. In other words, employers may not take adverse action against employees based on charges, warrants, allegations, etc.