Q. Can my relative claim my mother as a dependent?
A. Probably not. It's unlikely that the support test is met, since they live in her home. The value of her home ownership is considered support she provides to herself.
Nontaxable Social security doesn't count as income, for the income test, but social security money she spends on her self does count as support not provided by the relative, for the support test. Money she puts into savings & investment does not count as support she spent on herself. If no one person (or married couple) provides 50% of the support (for example you are also sending support), then a "multiple support agreement” (IRS Form 2120) can be used, to allow you to claim the dependent. https://www.irs.gov/pub/irs-pdf/f2120.pdf
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support value of a home is the fair market rental value, divided by the number of occupants. Utilities would be counted as additional support.
