Here's some facts for you. He took a new job AFTER he retired from UM. He is allowed to do that.
He retired and gave notice to UM. Later, the Ill coach found out that his expected AD was not going to take the job. The Ill coach then saw that Hauck had retired. He contacted Hauck. There was a delay of a day or two. Then they talked again and Hauck was hired. This is consistent with what has been said by the parties. The contract specifically says that he can retire (and then the liquidated damages clause doesn't apply).
Look at the contract. It doesn't prevent or prohibit Hauck from retiring or taking a new job. He's not supposed to actively look for a new job while employed by UM, without permission from the AD. The liquidated damages clause is not tied to that covenant not to seek a job. The only remedy would be an action for damages. What would the damages be?
"8. OTHER EMPLOYMENT. a. If more than six months remain of the term of this Agreement or any extension thereof, Coach agrees that he will not actively seek, negotiate for or accept other employment of an athletic nature without the prior permission of the Director of Athletics or the President of UM...."
"c. Coach may terminate this Agreement for any reason upon written notice to University. If such termination (other than by reason of retirement, death, disability, or incapacity) occurs during the term of this contract or any extension hereof, the University shall receive as liquidated damages an amount equal to Coach's Base Salary at the time of termination, multiplied by the number of years remaining ...."
[Again, the contract says the U shall receive liquidated damages, but doesn't say who is supposed to pay. Horrible drafting and failure to properly review the contract.]