probably - a lot more info is required so easiest way to get your answer is complete this IRS app - takes 2-3 minutes and you'll have your answer!
@JediMack - what happens if the children don't have SSNs? what happens if they are not US citizens?
That is why I responded with only 'probably'. it is best that OPs check the offical IRS app on these 'dependent' questions. there are simply a number of other requirements to claim the child.
If the children lived in your home more than 6 months, and they were placed there as foster children by the state or by an agency recognized by the state, then the children meet the relationship and residency tests to be claimed as dependents. (Note the placement must be official by the state or a state-approved agency, a voluntary arrangement between friends or relatives does not count.) If the children lived in your home more than half the year as foster children, it does not matter whether the biological parents' rights were terminated or not, what is important is the official foster placement and the duration (more than half the year).
As noted, there are other considerations to claiming a child, such as age, student status, and whether the child earns their own support. In the situation you described, the children would meet the relationship and residency tests, and now you need to analyze the other tests.
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