Can my husband get employment?

My husband worked for a company for 9 years and was fired on 12/14/15 well his boss said he quit, the unemployment office agreed he was fired from his position. He did not take the proper procedure to secure the day off and so he was let go. He has never had any kind of verbal or written warning in the past. He wrote his name on the calendar to be off and took off 8 hours on his time card and his boss said he didnt see it. Main thing is that he has never had any warning in the past, there was never any paperwork or handbook given when starting the job. Illinois has a law where they can terminate without reason at any time, will they be able to use this as a reason?