Illinois is an at will state. Which means you can fire someone just to fire someone. Now that will not stop them from suing you. Lord knows that there are attorneys who are just looking for a payday and will take just about any case.
What you should have in place in your HR manual is your policy for firing employees. Now we have been lucky and have had to only let two people go. They were good people, they just were not good fits for the structure of our office.
But unfortunately some of my clients have not been so lucky. One client had to let an employee go because they stopped coming into the office timely. This is a problem when they are supposed to be the first to arrive and set things up for others. So she had been warned verbally than received a written warning. Then she was let go.
The response from the employee was that she was being forced out because she was trying to live her life…
Employers have the right and need to expect that their employees will do what they are required to do when they are required to do it. If not the employee will suffer the consequences.
I only caution that you treat all employees the same. All expectations are equal and they all consequence are equal and they match your policies and procedures manual and you should be in good shape.