My daughter-in-law just received her W-4 and realized that Federal Taxes were not taken out the whole year. Social Security and Medicare Taxes were though. None of the employees received a payroll stub the entire year to be able to notice this. What can she do and what is she liable for? What is the company liable for?

I assume she got her W-2 (W-4 is what you submit to dictate withholding to the employer).

There is little she can do. She is liable to pay the federal (and state, if applicable) income taxes. She may be able to avoid an under-withholding penalty if the company admits they messed up by not withholding.

The company may be subject to some IRS fines for not withholding the money, but other than that, they have no liability.