Then he can still claim Head of Household and claim her. Since an insufficient amount was withheld, he can back off some of these exemptions.
Checking Your Withholding After you have given your employer a Form W-4, you can check to see whether the amount of tax withheld from your pay is too little or too much. If too much or too little tax is being withheld, you should give your employer a new Form W-4 to change your withholding. You should try to have your withholding match your actual tax liability. If not enough tax is withheld, you will owe tax at the end of the year and may have to pay interest and a penalty. If too much tax is withheld, you will lose the use of that money until you get your refund. Always check your withholding if there are personal or financial changes in your life or changes in the law that might change your tax liability. PUB 17
Here is a complete explanation of how W-4 works: W-4.
