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Sorry, I did some further research.  See page 15 and page 20 here, <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p501.pdf">https://www.irs.gov/pub/irs-pdf/p501.pdf</a>
"Support provided by the state (welfare, food benefits, housing, etc.)."  

SSDI is taxable because it is in the place of taxable wages and is only provided to people who have worked enough credits.  Therefore it is handled as taxable wages, although most recipients don't get enough to actually go over the personal exemption and standard deduction.  That makes SSDI "support provided by the child" without question.

SSI is strictly need based.  That would make SSI "support provided by the government."  However, as noted in this article, SSI will be reduced if your child receives support from you, unless you enter into a calculation with the government to show the child as paying their fair share of living expenses.  <a rel="nofollow" target="_blank" href="http://www.stepnowskilaw.com/DependentExemption.html">http://www.stepnowskilaw.com/DependentExemptio...>

That creates a complex situation. If you tell social security that your child is living with you and you are taking care of him, that reduces his need and may reduce his need based payments.  If you tell the government that he is paying for his own rent, utilities, etc. (either living on his own or as an equal share of your expenses), then that increases his need and keeps the SSI payments high, but shows to the government that he is "paying his own way."  I have found various web sites go both ways on SSI, that it does or does not count toward "paying half his own expenses."

I see above that @Hal_Al might have a different opinion from mine on SSI.

None of this matters if his expenses are high enough.  You need to start with the chart on page 16 of publication 501.  Add up the expenses for the entire household (rent, utilities, food, repairs).  If you own, you don't include mortgage and property taxes; instead, you use the fair market rental value -- what someone would pay to rent a similar home in that neighborhood.  Divide all those household expenses by the number of people living there.  Then add his personal expenses (clothes, medical costs not covered by insurance, recreation, etc.)

Since his benefit is $864 a month, then if his total living expenses are more than $1729 per month, then you pay more than half, and he does NOT pay more than half, no matter what kind of dependent he is or how the SSI is counted.

If his living expenses are less than $1729 and his income is SSDI, then he pays more than half and he is not a dependent.  If his living expenses are less than $1729 and his income is SSI, then it is still probably "support provided by him" because of the use it or lose it nature of the payment, as you first described.  However, there are some web sites that claim that you don't have to include SSI as support, so you could follow that and hope you don't get audited.


And finally, while I read a lot, and have answered over 10,000 tax questions on this forum over the years, I'm really just a stranger on the internet.  For a definitive answer you should look for an accountant or enrolled agent who handles disability issues.