I have a 21 yr old grandaughter and 21 mo great grandson living with me for the past few years but I was told that I could not claim as she is receiving state monies for her addictions. We have spent over $7000 per year to aid in supporting her and her son. She gets about $375 mo cash and $250 food stamps.

The sad thing about this is in order to claim them they will lose support from the state. In order to be able to claim them she has to sign guardianship of herself over to you (at least in my home state that is the case). The mental health clinic and the social services department in your home state should be able to walk you through this process. I was in a similar situation before, but by the time I added it altogether- in my situation at least - it was better for us financially due to doctor bills and etc to leave it as it was.
Personal note - I dealt with addiction to 8 yrs ago to cocaine and overcame it without any help. It took me a good while to overcome the emotional addiction. Narcotics Anonymous did wonders for me, so did AA. However, unless the rules changed to AA you cannot state you are an addict. The meetings between the 2 are very different in my opinion, and a lot can be learned from attending both.

To claim your 21 year old granddaughter her annual gross income must be less than $3650. If the money she receives is taxable then her gross income exceeds that amount. But if these are welfare or public assistance payments (which are not taxable) and she has less than $3650 in taxable income you can claim her as a dependent IF you provided more than half her support. Since she already gets about $6300/yr in payments and food stamps, the question is whether you provide an additional amount of financial support that is greater than that?

As for the great grandson - you can claim him only if his mother and father do not.

Thanks, I thought that was the case but our cashflow is hurting as she is not the best with managing money let alone any other part of her life. Enjoying the little great grandson is our only reward for now.
Thanks for the insight on your experience. She does attend meetings of both organizations but not regularly yet she says she gets encouragement from them.