Illegals get to deduct children living in Mexico, or wherever? That is absurd.
Let me try to clarify.
Illegals apply for an ITIN in order to file a tax return. You cannot claim EITC when filing an ITIN, but prior to the PATH Act passed last year, you could claim the additional child tax credit. Illegals can no longer claim this credit when filing tax returns.
Prior to last year, a typical ITIN return might look like this. The filer might file head of household and list four or five dependent children, also with ITINs. The adjusted gross income on the return is typically somewhere in the teens or twenty thousands dollar range. After exemptions, the taxable income is frequently zero, but the unused child tax credit ($1,000 per child) could be claimed as a refundable credit called the additional child tax credit.
Let's say the AGI was $25,000 and the return filed head of household with four dependent children. After the standard deduction and exemptions, the taxable income is zero. The unused portion of the child tax credit would be $4,000.00. The filer would receive a refund of any withholding tax plus up to $4,000.00. It is very possible none of the four claimed dependents resided in the US at the time the return was filed, but no way to verify. So in actuality, the filer did pay social security and medicare taxes (payroll taxes) which would amount to about $1,700 or so, but received $4,000 courtesy of the US taxpayer. My experience is that the majority of ITIN returns filed looked similar to this.
Now that the Path Act has been implemented, they are out of luck. However, once they are granted a social security number, the additional child tax credit and the EITC credit becomes available.