If you had no income during the tax year, there would be no tax benefit to you claiming the children as dependents. You would not qualify for any tax credit and you have no withholding to be refunded. In addition, if you had no income during 2015, you would not be required to file a tax return.
Unfortunately, since you are not married, the IRS will likely take any past due obligations that are owed. However, it would still be beneficial for the father to claim the dependents even if the refund is taken. This will just pay off the debts quicker.
If you were married, you could file an Injured Spouse Claim and receive your "portion" of the refund back from the IRS.
Your boyfriend may be able to claim you as a dependent if you lived together for the entire year, he provided more than 50% of your support and your gross income was less than $4,000. There are a few other eligibility requirements. This is known as a qualifying relative as opposed to a qualifying child. However, it would give him an additional $4,000 deduction from his income.
Please see the link below for more information on the requirements for a qualifying relative.
Qualifying
Relative Requirements
