On Urban Meyer situation!
Every coach has a clause in his contract that requires he act in accordance with the conduct expected of someone in his position. Most go on to say something along the lines that a university, in its sole discretion, can fire the coach for cause if his actions adversely affect the image of the university. There is a Title IX-related clause in his contract that deals with his reporting staff misconduct, but that was not inserted until he signed his extension earlier this year and the alleged incidents happened in 2014 and 2015. There could be a broader university policy for all employees that might apply.
It should also be noted that Ohio State is at the center of a pair of sexual assault/harassment cases right now, one involving a former team doctor and one involving a former assistant dive coach. While the incident with the former football assistant does not appear to be sexual in nature, it is another black eye for the university and its athletics department, which has shown in the past that it is not afraid to terminate a successful coach at an inopportune time. Look at the timing of when Gene Smith fired Jim Tressel and Thad Matta.