My daughter made 10,000 this year. And she haven't had federal taxes taken out of her check at all. She did claim her and her two kids which she haven't taken care of for two years, but they did take out state taxes out of her check. Do she have to pay federal back.

It is illegal to claim exemptions to which you are not entitled.

Whether she owes taxes depends on her exemptions, deductions. The bracket for $1,000 and less is roughly 10%, depending on exemptions and deductions.

While she should NOT have claimed the exemption for her children, the combination of her personal exemption ($3,650) and the standard deduction ($5,700) means the first $9,350 is tax-exempt.

With only $650 of taxable income, she will get a refund because she qualifies for the $400 Making Work Pay Credit and probably the Earned Income Credit, especially if either of the children lived with her and she can claim Head of Household.