Please see Champ Hal-Al's answer below:
Q. Can anyone claim her as a dependent?
A. Simple answer: no. As you already realized, to be a "qualifying child" dependent (and qualify for the child tax credit and Earned Income Credit) the child must have lived with a close relative (including a foster parent) for more than half the year.
That said, it's possible that the child could be a "Qualifying Relative" dependent if a close relative (including a foster parent), provided more than half the child's support for the year. But a Qualifying Relative only gets you the $500 (on refundable) other dependent credit; not child tax credit or earned income credit.
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit.
They are interrelated but the rules are different for each.
The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
Rules for Claiming a Dependent on Your Tax Return
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