relative claim mother

Possibly.  If this person pays over half of her expenses, depending on how they are related to her and how long they lived with her, they may be able to claim her as a dependent on their return.  If the criteria below is met, they would be able to claim the $500 Other Dependent Credit and possibly claim Head of Household. 

To claim someone as a Qualifying Relative, they must be:

• Your child ( including step children, adoptive children and foster children) or a descendent of them
• Your sibling (including half siblings) or a child of your sibling or a sibling-in-law
• Your parent or grandparents, including step parents and in laws
• Any other person that lived with you for the entire tax year
• Not a qualifying child of another taxpayer
• Someone that you provided over half of their support for during the tax year
• Has less than $5,050 in income (not counting social security)

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.